Question

Find the value of the following:

Answer 1

$i = \sqrt{ - 1}$
$i {}^{x} = 1 \: if \: x \: is \: multiple \: of \: 4$
else it is-1
$so \: i {}^{2} + i {}^{4} + {i}^{6} .......$
can be expressed as
$- 1 + 1 - 1 + 1......$
If no.of term is even then sum is 0 else if it is odd then value is-1.As no.of term is 2n+1 which is odd so value of series is -1
Ans: -1
Hope this helps : )

Answer 2

-1 can be your answer