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Suppose n is a natural number such that ...

Suppose n is a natural number such that `|i + 2i^2 + 3i^3 +...... + ni^n|=18sqrt2` where `i` is the square root of `-1`. Then n is

A

`9`

B

`18`

C

`36`

D

`72`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `S=i+2i^(2)+3i^(3)+…….+ni^(n)`………..`(i)`
`:. iS=i^(2)+2i^(3)+3i^(4)+…….+ni^(n-1)`…………`(ii)`
Subtracting, we get ,brgt `S(1-i)=i+i^(2)+i^(3)+………..+i^(n)-ni^(n+1)`
`=(i(1-i^(n)))/(1-i)-ni^(n+1)`
Now put the values of `n` and verify.
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