Question

2²+4²+6²+8²+10²=....? 1²+3²+5²+7²+9²+11² =....? 1²+2²+3²+.....+11²..​

Answer 1

Step-by-step explanation:

What is the sum of[math] 1^2-2^2+3^2-4^2+5^2-…+21^2[/math]?

in this question,

(sum of the sq. odd no.) - (sum of the sq. of even no.)

(1^2+3^2+5^2……21^2) - (2^2+4^2+6^2…..20^2)

sum of the sq. of odd no. = n(2n-1)(2n+1)/3

sum of the sq. of even no. = 2n(n+1)(2n+1)/3

for odd no. n = 11

for even no. n= 10

11(2*11–1)(2*11+1)/3 - 2*10(10+1)(2*10+1)/3

1771 -1540

191