Question

Evaluate the following:-
$\frac{1}{i} + \frac{1}{ {i}^{2} } + \frac{1}{ {i}^{3} } + \frac{1}{ {i}^{4} } + ........... + \frac{1}{ {i}^{20} }$

Answer 1

by sum of GP a( r^n - 1) /(r-1)
1/i + 1/i^2 .......+1/i^20 = 1/i(1/i^20-1)/(1/i-1)
since 1/i^20 = 1
thus sum = 1/i (1-1)/(1/i-1) = 0