Question

The value of ${\sum }_{n=1}^{2015}{i}^n$ is

• A. -1
• B. 2i
• C. 2
• D. -i

Answer 1

The correct option is A

-1

${\sum }_{n=1}^{2015}{i}^n$ = $i+i^2+i^3+..........................+i^{2015}$

We know that sum of 4 consecutive powers of i is zero

ie, $i^n+i^{n+1}+i^{n+2}+i^{n+3}$ = 0

So, as every 4 times to zero, all the terms upto $i^{2012}$ will get added to zero

So, ${\sum }_{n=1}^{2015}{i}^n$ = $i^{2013}+i^{2014}+i^{2015}$

= $i^1+i^2+i^3$ = $i-1-i$

= -1