Simplifying Exponents

dlencz wrote:3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =


(A) 3^7

(B) 3^8

(C) 3^14

(D) 3^28

(E) 3^30

We can write 3 + 3 + 3 = 3²
= 3² + 2 * 3² + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7
= 3² + 2 * 3²(1 + 3 + 3² + 3^3 + 3^4 + 3^5)
1 + 3 + 3² + 3^3 + 3^4 + 3^5 is a geometric series and sum to the nth term = a[r� - 1]/(r - 1) = 1(3^6 - 1)/(3 - 1) = 728/2 = 364
So, 3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7
= 3² + 2 * 3² * 364
= 3² + 3² * 728 = 3²(1 + 728) = 3² * 729 = 3² * 3^6 = [spoiler]3^8[/spoiler]

The correct answer is B.