Question

Consider the series 2 - 4 + 8 ..<br />
Find the sum of the first 10 terms​

Answer 1

-682

Explanation:

`S = 2 - 4 + 8 ... \\ \\ S= 2^1-2^2+2^3-2^4+2^5+...+2^9-2^(10)\\ \\ b_1 = 2, \quad q = -2,\quad n = 10 \\ \\ S = (b_1\cdot (q^(10)-1))/(q-1) = (2\cdot \Big[(-2)^(10)-1\Big])/(-2-1) = (2^(11)-2)/(-3) = (2046)/(-3) = -682`