Latest CAT Aptitude Question SOLUTION: solve [2+1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]

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[2+1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]

Asked In CAT satyanarayana (11 years ago)

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revendera  (11 years ago)

[2+1] can be written as=[2^2-1]
[2+1][2^2+1] can be written as=(2^4-1)
thus
[2+1][2^2+1]
2^4+1)(2^8+1)(2^16+1)....[2^256+1]
can be written as=[2^512-1]

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sainath  (11 years ago)

[2+1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]
=[3][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]
=[4-1][2^2+1][2^4+1][2^8+1][2^16+1]...........[2^256+1]
=[4-1][4+1][2^4+1][2^8+1][2^16+1]...........[2^256+1] [since(a+b)(a-b)=a^2-b^2]
=[16-1][2^4+1][2^8+1][2^16+1]...........[2^256+1]
=[16-1][16+1] [2^8+1][2^16+1]...........[2^256+1]
.
.
.
in this way finally we remain with
=[2^256-1][2^256+1]
=2^512-1

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