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Let f : N rarr R be a function such that...

Let `f : N rarr R` be a function such that `f(1) + 2f(2) + 3f(3) + ....+nf(n)= n(n+1) f(n)`, for `n ge 2` and f(1) = 1 then

A

`f(n) = (1)/(n)`

B

`f(5) = (1)/(10)`

C

`f(5) = (1)/(5)`

D

`f(n) = (1)/(2n)`

Text Solution

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The correct Answer is:
B, D
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Knowledge Check

  • Consider the function f defined on the set of all non-negative interger such that f(0) = 1, f(1) =0 and f(n) + f(n-1) = nf(n-1)+(n-1) f(n-2) for n ge 2 , then f(5) is equal to

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