[Music] Haemon Akiyama in this video I discussed natin company medieval wait given an submission edition so in this video motto to to tire company oh Mack substitute or assault and summation notation so first and wobba Sigma notation so a Sigma Edition is a more concise way to express the sum of a sub 1 up to a sub n or you see it is not in italic nothin this is a we can you make use of summation notation or Sigma notation okay and by you Sigma notation so this is a Greek letter so as you can see it looks like letter e and it is called Sigma which tells us to sum or add up the terms so pag maritime summation notation or Sigma u symbol 9 Sigma atomic Sasabe that we have to all add all the terms in a series okay so what are the parts of Sigma notation okay given this example your key is your index of summation or ito yung start orient init about nothing lower limit X in a be netting index of summation or young Simula d2 Taiyo unum mugs a substitute come under young numbering and and Ito so it is similar and then your end is the end or Utena tog netting upper limit so a toy you maxis I become Hangang a new number you is a substitute not in d2 sir okay okay so again a token a toge entirety substitute number namaha attendee to sake index of summation at Kong Hong Kong Sansa that is your n Union and or upper limit let's have an example so let us try to find an evil wait okay so I have here five K so ibig sabihin five times K and biome K so Athens in 1802 Runa if it's a BN young Caine attend maximal a fossa one hung Gong for Sola haughty and the Hat gnome terms nuttin yeah aDNA ten now you cannot in eat the times not in the hats of five so had in bagua since one to forty oh so much the substitute Iona one to four don't forget it must be the sum or you are going to add all the terms so do not forget the plus sign okay so we will now have five times 1 that is 5 by 5 times 2 that is 10 so 5 times 3 that is 15 and 5 times 4 is 20 so ibig sabihin we will have 50 so the summation of 5 K or five times K from 1 to 4 is equal to 50 next so I have here the summation of 3 K plus 1 or 3 times k plus 1 from 1 to 6 or D tournament on cane attend a maximal adult I set to 1 and then we will end with 6 so given this expression so 3 K plus 1 I'm LL again attendance a chemically similar Taizo one Matata pasta esse 6 kasi Union NASA Sigmund attend ok so let us now simplify we will have 3 times 1 that is 3 3 times 2 that is 6 this is 9 12 15 and 3 times 6 is 18 so we will now have 3 plus 1 is 4 6 plus 1 is 7 9 plus 1 is 10 12 plus 1 is 13 15 plus 1 is 16 and 10 plus 1 is 19 so we will now have we will add all the terms we will have 69 next the summation of K squared or the square of K from 0 to 4 so we will have K squared so under UK and in Allegan attend maxi simulit is 0 Cassie Union Ajala guy McIntyre for okay just follow the expression come K squared Eddie ibig sabihin the number n is a substitute more and then squared ok come a new number Dignan Miyoung lower limit at upper limit monza and maxi similar Atkinson and Matata pause so we now have 0 squared is 0 1 squared is 1 2 squared is 4 3 squared is 9 and 4 squared is 16 so we will add all the terms we will now have 30 because 16 plus 9 is 25 plus 4 it's 29 plus 1 that is 3 T next I have here the summation of negative 1 raise to K plus 1 from 1 to 5 so we will now have Sola had negative 1 tile raise to K plus 1 so a big Sabine don't IMAX a substitute say exponent yeah so I know young alala gain a teens exponent now you add nothing someone so the based on the given it starts from 1 to 5 so we will substitute 1 2 3 4 & 5 so in the middle again at an expression I in a baby's lung tired and sad woman on givin okay so nagrel'a Galen ironing number or digit now is a substitute done sake there is Indian attention Papa fella man so since my negative 1 K Janet one unit elana game again so let us now simplify we will have negative 1 raised to 1 plus 1 that is raised to 2 and then negative 1 raised to 3 cos a 2 plus 1 and then 3 plus 1 we have 4 4 plus 1 we have 5 + 5 + 1 we have 6 okay simplify not n we have negative 1 raised to 2 that is positive 1 negative 1 raised to 3 that is negative 1 negative 1 raised to 4 that is positive 1 negative 1 raised to 5 that is negative 1 and negative 1 raised to 6 that is positive 1 now and short cut the top arahida time ëletís assign if the exponent is an even number the product is always positive if it's odd number the product is always negative Kyah Huma Poppins in your the exponent not in a to 4 at 6 you product not n is positive okay so we will now have 1 plus negative 1 that is 0 and then 1 plus negative 1 again that is still 0 so that what's left is 1 let's have another example okay so we have the summation of K cube all over k plus one so much a substitute is a numerator at denominator so hindi neelam isa and Allegan attend since Mirren tyonne case a numerator and denominator so we will have so Santa you max is similar from zero so the numerator at denominator because a Makita Yan both parts of the fraction so from zero to three I N and then we will simplify so we will have 0 raise to 3 that is 0 and then 0 plus 1 that is 1 so 0 / 1 1 raise to 3 that is 1 1 plus 1 that is 2 so we have 1/2 turista tree is 8 and then 2 plus 1 that is 3 so 8 over 3 and then 3 raise to 3 is 27 over 3 plus 4 that is 4 so 27 over 4 equals 119 over it will get the LCD the LCD is 12 and then simplify Hey next I have here the summation of negative 1 raised okay over K okay so hogaya annemun canina de la bikina la laguna dynamics a substitute IO Peru is a Tito I exponents oh hi Anna so Marin tyonne case a numerator and denominator pero Anana BAM in Allegan 18 semana kan of course we will start from 1 to 5 so don't forget the King in the numerator it's just an exponent okay and then 2 or 3 4 5 hey so Sunday night in you I know your pattern you rule okay and then simplify negative 1 raised to 1 is 9 they've won over 1 negative 1 raise to 2 is positive 1 over 2 or 1/2 so hey guy anissina Beco Hanina if the exponent is an even number the product is positive if it's an odd number the product is negative ok so next so negative 1 is odd numbers are so negative 1 and then over 3 and then 4 is an even number so positive 1 over 4 and then we all we all have negative 1 raised to 5 so that is negative 1 over 5 okay so for map up and sing your canopy Illuminati in the nominee Choi died wala naman philemon is also denominator so we now have negative 1 over 1 that is negative 1 and then just copy 1/2 1/3 so you wanted not a negative 1/3 Musharraf I say a nut n plus and then times negative so that is negative and then plus and then plus so we now have get the LCD simplify we have negative 47 over 60 thank you for watching this video I hope you learned something don't forget to Like subscribe and hit the bell button so our Walmart Channel just keep on watching