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If (1+x)(1+x^2)(1+x^4)(1+x^(128))=sum(r=...

If `(1+x)(1+x^2)(1+x^4)(1+x^(128))=sum_(r=0)^n x^r` then `n` is equal to `256` b. `255` c. `254` d. none of these

A

255

B

127

C

63

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`(1+a)(1+a^(2))(1+a^(4)) . . . . (1+a^(128))=underset(r=0)overset(n)suma^(r )`
`rArr" "` n=Exponenet of the highest power of a
`rArr" "n=1+2+4+ . . . .+128`
`rArr" "n=1+2+2^(2)+ . . .. +2^(7)=((2^(8)-1)/(2-1))=255`
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