`f : N -> R` be a function satisfying the following conditions: `f(1)=1` and `f(1)+2.f(2)+3.f(3)+........n.f(n)=n(n+1)f(n)` for `n>=2` The value of `f(1003)` is `(1)/(K)` ,where K equals

If (1)=1 and f(1)+2f(2)=3f(3)+......nf(n)=n(n+1)f(n) Then find the value of 49f(49)

A Function f is defined for all positive integers and satisfies f(1)=2005 and f(1)+f(2)+.........+f(n)=n^(2)f(n) for all n>1. Find the value of f(2004)

Let f: N to R be a function satisfying the condition f(1) + f(2) ……………. +f(n) = n^(2) f(n) AA n in N If f(2025) = 1/(2026) , then f(1) = ………….

Let f:N rarr R be a function such that (ii) f(1)+2f(2)+3f(3)+.........+nf(n)=n(n+1)f(n)=n(n+1)f(n)AA n>=2 Then find f(2011)

Consider a function f(n) defined for all n in N. The function satisfies the following two condition (i) f(1) + f(2) +f(3)+.....to oo =1 (ii) f(n) = {(1-p)p^(-1)}(f(n+1)+f(n+2)+....+oo), where 0ltplt1 the f(2) is equal to

Let f:N rarr R be such that f(1)=1 and f(1)+2f(2)+3f(3)+…+nf(n)=n(n+1)f(n), for n ge 2, " then " /(2010f(2010)) is ……….. .

If   f(x ) = n/( n+1) , then find the value of f(n) + 1/f(n)

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

If f(1) = 1 and f(n + 1) = 2 f(n) + 1, if n ge 1, then f(n) is.

If f is a function satisfying f(x+y)=f(x)xx f(y) for all x,y in N such that f(1)=3 and sum_(x=1)^(n)f(x)=120 find the value of n