Question

Write the sum of the series $i+i^2+i^3+.......$ upto 1000 terms.

Answer 1

$i+i^2+i^3+.....\text{upto 1000 terms}=i+i^2+i^3+i^4+....i^{1000}=0[\because i^n+i^{n+1}+i^{n+2}+i^{n+3}=0,\text{where}nϵNi.e.,{\sum }_{n=1}^{1000}{i}^n=0]$