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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
`{:(S=i+2i^(2)+3i^(3)+....+ni^(n)),(ul(iS=" "i^(2)+2i^(3)+....+(n-1)i^(n)+ni^(n+1)" ")),(S(1-i)=i+i^(2)+i^(3)+....+i^(n)-ni^(n+1)),(S(1-i)=(i(1-i^(n)))/(1-i)-ni^(n+1)rArr S=(1-i^(n))/(-2i)-(ni^(n+i))/(1-i)),(" "darr" " darr),(" "Z_(1)"(say) "z_(2) "(say)"):}`
`|z_(1)|=1/sqrt(2)` or `0 |z_(2)|=n/sqrt(2)=n/2 sqrt(2)`
`n/2=18 rArr n=36`
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