Question

please solve this question​
k=1 and n(if the photo is unclear)

Answer 1

Step-by-step explanation:

see your need 2 formulae for this question:

(i)- the sum of all natural numbers till n=n(n+1)/2

(ii)- the sum of the squares of all the natural numbers till n=n(n+1)(2n+1)/6

for example:

1+2+3+...+8= 8(8+1)/2= 36

1²+2²+3²= 3(3+1)/(2*3+1)/6= 14

using the same formulae to find the value of n:-

{(n(n+1)(2n+1)}/6 ÷ (n(n+1))/2=17

(2n+1)/3=17

n=25

now,one more to understand,

summation(sigma){2k-1)=(sigma)(2k) - (sigma)(1)

=>2(sigma)(k) - sigma(1)

=>2k(k+1)/2 - k

=>2*25*26/2 - 25

=>625

THINGS TO UNDERSTAND:-

sigma:-it is the symbol which denotes summation(addition).in the picture,it is shown as capital M rotated 90° in anti clockwise direction.

whenever we are given,a general term of the series which is combined in ± form,then we can use the same methodology. we can't use this when the general term is given in product form..

for example:

sigma(k) means 1+2+3...+k

sigma(constant) means k+k+... n times =n k

sigma(k²) means 1²+2²+3²...+k²=k(k+1)(2k+1)/6