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The value of sum(n=0)^(100)i^(n!) equals...

The value of `sum_(n=0)^(100)i^(n!)` equals (where `i=sqrt(-1))`

A

`-1`

B

`i`

C

`2i+95`

D

`97+i`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `S=sum_(n=0)^(100)(i)^(n!)`
`=(i)^(0!)+(i)^(1!)+(i)^(2!)+…..`
`=i+i-1+i^(6)+i^(24)+(i)^(5!)+(i)^(6!)+..+(i)^(100!)`
`=95+2i`
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