Question

Find the value of the sum $\sum _{n=1}^5(i^n+i^{n+2})$ where $i=\sqrt{-1}$

Answer 1

$\sum _{n=5}^{n=1}(i^n+i^{n+2})$

$(i+i^3+i^2+i^4+i^3+i^5+i^4+i^6+i^5+i^7)$

$=(i-i-1+1+1-i+1+1-1+i-i)$

$=0$