Question

Compute the sum:

81
∑ (2i-1)
i=1

Answer 1

81
∑ (2i-1)
i=1

= 2∑i - ∑1
= 2*81*82/2 - 81 = 6561

since you know that

n
∑i = n(n+1)/2
i=1

Or, working with the sum as an AP, you have

a=1
d=2

S81 = 81/2 (2+80*2) = 6561

Or, note that you have the sum of the first 81 odd numbers. That sum is 81^2 = 6561