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The greatest +ve integer k, for which 4^...

The greatest +ve integer k, for which `4^k+1` is factor of sum `1+2+2^2+....+2^(99)` is

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The correct Answer is:
25
`1+2+2^(2)+….2^(oo)=2^(100)-1`
`=4^(50)-1=(4^(50)-1)(4^(25)+1)`
`therefore" "k=25`
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