[Music] hi Monica wama in this video we will define series finite series and infinite series we will also express a series in Sigma notation so first what is a series a series is the sum of the terms of a sequence so again I'm series ito yung some nominal terms given an sequence so Marin consequence begin add not in China in teen atomic Nattie series so halimbawa I have here 1 3 5 7 9 and 11 this is just a sequence pair of a pug in AD not in Shaa Italian anti-natal Wagner in series so young-sam yeah that is there that is an example of series okay I have here a sub six so since Y ni6 so FX a be hand we will get the sum of the first six terms so it's a one three five seven nine at eleven kakuni not in young-sam Neela since atonium Annina a first six terms nothing off a bucket first six terms kasam malaga ito i6 as S sub six alright an infinite series is the sum of the terms of a sub 1 plus a sub 2 and so on and so forth so forma Poppins in nofap ignorant 'young infinite sequence then madinat and a infinite series next a finite series also called partial sum so a tournament packs in a be nominating partial sum or finite sea Conan ad Newsome no sequence not enemy room ending okay so cappuccino Honiton young son and finite sequence finite series and dog not in done in the sequence 1 3 6 10 15 we have the following partial sums so halimbawa i have a sub 1 so I'm first I'm not in a 1 the first term of the sequence a sub dweeb exhibition 1 plus 3 equals 4 y 1 plus 3 because this is the sum of the first two terms as a 3 we have 1 plus 3 plus 6 equals 10 because this is the sum of the first three terms so4 1 plus 3 plus 6 plus 10 is equal to 20 the sum of the first four terms and s of 5 we have 1 plus 3 plus 6 plus 10 plus 15 is equal to 35 because that is the sum of the first 5 terms so depending on illuminance S sub 3 so first three terms as sub 4 first four terms another example as sub two ibig sabihin the sum of the first two terms on a young fresh two terms not n we have 5 and 15 so therefore we will have pi plus 15 that is 20 s of 4 is equal to the sum of the first four terms you Munim Appa so S sub 4 we have 5 plus 15 plus 25 plus 35 and that is 80 another example as a poor so we will get the sum of the first four terms so we have - negative 6:18 and negative 54 so we will now have two plus negative six plus 18 plus negative 54 and that is equal to negative 40 s sub 6 is the sum of the first six terms so we will know how it's a salmon anathan see 162 and negative 486 so we will have 2 plus negative 6 plus 18 plus negative 54 plus 160 2 plus negative 486 and that is equal to negative 364 so Gannon lamb all right Sigma notation what is Sigma notation a toy Emperor and unpack sulit natin man series so since i'm gonnago one attends a series I in ad not inches and a hat Latin terms therefore we can make use of summation notation or Sigma notation n-nobody tour this is the Greek letter so parish and letter e nothing at about nothing Sigma which tells us the sum or add up the terms of a pagina gamete net income symbol Neto shy inaccessible now we need to add all the terms okay so atrium concise way of expressing a series so Anna battle open Abishag inugami so the summation of three times key starts with a taeyeon so a token at o-18 tina tavad nadine index of summation packs in a be nothing index gentile maxi Simula orient in atomic nothing lower limit so young kein Ayin young young number come santa yo maxi similar max substitute the once at a time scale so halimbawa that is k is equal to 1 so I'm gonna nothing gagawin 3 times 1 ok come sir anti Yamata tapas Union young Andaman Shyam and Gentile Matata paws are you Tina tawa did nothing upper limit so hidimba wa n is equal to for a big Sabean Matata post is a three times four so come on chemo is equal to 1 and your n is equal to 4 therefore and McGee ging Sammy summation mu I 3 times 1 plus 3 times 2 plus 3 times 3 plus 3 times 4 so meta kappa Spicer for Casilla n mo i for okay now hindi l'm locking key and inna gamut nothing symbol weather in tango muhammad nam i weather in j so fight a new letter pero a model a schema gamete i I J or K ok let us try to express each Psalm using Sigma notation so give the new series and nothing shall express using Sigma notation so halimbawa marina hadith on 1 plus 1/2 plus 1/3 plus 1/4 plus 1/5 so Buffett ganito and summation notation so again ding-ding Yahoo under your pattern since you given that in a series in a fraction form therefore fraction form brain cha ok now Buffett 1 and Allah gave us a task as he put one on the pop and Cena tense at a school when Eunice a numerator now it on key bucket key atonium key concern Malala Manhattan cumson maxi see mullah Atkinson Matata pause so Kayla delegate not engine oh there one can say all of the numerators I won UK since a by Bashar km ill allah gave methane at veto not in Alana Jenkinson maxi similar okay now we all know that one item 1 and denominator Union I won so epic Sabine's r1 shinnok similar at NAPA Oh scheisse fine okay so he didn't go so is one soon Atlanta is a pattern since the numerator not in a 1 and then UK Gentile Maga assign come son Max is Ebola at Matata pose so next touches a one again chesa 5 so this is now our summation notation for da given series next so I have here 1 squared plus 2 squared plus three squared plus and squared okay so I know gotta be nothing so look at the pattern I'm partnering at in so it okay gentlemen assign comes and maxi similar Atkinson Matata pose so a delegate not in K and then since my square jaw so I'm simple not in yo and I K squared okay honking at us and that insha'Allah a guy so since next in Malaysia so 1i n sy Bacall Yamuna Sabah back on son come axis Imola and then sunshine at a post since wallet I am Number John ensure so n and illaallah game at engine hey so next arch is a 1 again chess again this is our symbol next okay I have here 1 plus negative 3 plus 5 plus negative 7 ok so much of complicated data Noah perros again it proved not and Buffett at all so funny not in summation notation attend at a summation notation so next arches are one neg inches of war so max a substitute is Imola 1 hung them for cousin came at in a1 and you mess at us not in eye for so let us pray to substitute from 1 to 4 so a Tanisha negative 1 raise to K plus 1 times 2 K minus 1 so a substitute not in C 1 cos ASA be dito ka is equal to 1 MUX type note is a 1 so substitute nothing see once among a key so Maggie game 1 plus 1 and adding exponent and then you took a nut in Maggie 2 times 1 so let us all Maggie negative 1 raise to 2 and then 2 times 1 that will become 2 and and bring down minus one so we will have negative one squared is positive 1 and then 2 minus 1 that is also positive 1 so 1 times 1 is equal to 1 check not n okay that is our first term next let's try to substitute to NASA tuple entire so my gigging yum K + 1 hat in McGinn 2 + 1 u - k not in McGinn 2 times 2 so to mnemonic is a substitute not in neon so we will have negative 1 raised to 3 and then 2 times 2 that will become 4 and then minus 1 so negative 1 raised to 3 is still negative 1 and then 4 minus 1 that is 3 so therefore negative 1 times 3 that is negative 3 and this is our second term ok next so again since Sangam a purchase or nasa triple entire so sorry substitute not in see Theresa K + 1 and then 2 K Maggie gain 2 times 3 so we will have negative 1 raise to 4 and then 2 times 3 we have 6 plus minus 1 so negative 1 raise to 4 is positive 1 and then 6 minus 1 is 5 so therefore we will have 1 times 5 is equal to 5 and that is our third term next okay so at Onalaska say you knock NASA some issue annotation a 10-4 unless and more limit so you own NASA at the ass so we will now have substitute not in C 4 so 4 plus 1 an exponent not n and then 2 times 4 so let us compute so 4 plus 1 that will become 5 and then 8 a 2 times 4 that is 8 so minus 1 therefore we will have negative 1 raised to 5 that is still negative 1 and then 8 minus 1 that is 7 so that is equal to negative 1 times 7 and that is negative seven and that is the fourth term thank you for watching this video I hope you learned something don't forget to Like subscribe and hit the bell button to our wall my channel just keep on watching