Question

solve the problem fast

Answer 1

$i^{n} + i^{n+1} = i^{n} (i+1)$
As we know that
$1 = i^{4n}, i = i^{4n+1}, -1 = i^{4n+2}, -i = i^{4n+3}$
sum from n =1 to 13, we get
= 4(i-1-i+1) .            + i
for first 12 terms .  last 13th term
= i
So your answer is i(i+1) = i-1
the Option 2)