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$i^{2}+i^{3}+.......+i^{4000}$=

Answer:

Explanation:

$\because$    $i^{n}+i^{n+1}+i^{n+2}+i^{n+3}=0,\forall n \in Integer$

So, $i^{2}+i^{3}+i^{4}+.........+i^{4000}$

 = $-i+[i+i^{2}+i^{3}+.....+i^{4000}]$=-i