Question

Prove without using a formula,that the sum of the series
3^2+3^4+3^6+......to 20 terms is given by S20=9/8(9^20-1)

Answer 1

3^2 + ... + 3^40
= 9^1 + 9^2 + ... + 9^20
Now, you know that (x-1)(1 + x + x^2 + ... x^(n-1)) = x^n - 1