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If f(1)=1 and f(1)+2f(2)=3f(3)+......nf(...

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

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`f(1) = 1`
`f(1)+2f(2)+3f(3)+...+nf(n) = n(n+1)f(n)`
`:. f(1)+2f(2) = 2*3*f(2)`
`=>f(1) = 4f(2)`
`=>1 = 4f(2)`
`=>2f(2) = 1/2`
Now, `f(1)+2f(2)+3f(3) = 3*4*f(3)`
`=>1+1/2 = 9f(3)`
...
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