The sum of 50 terms of the series `1+2(1+1/(50))+3(1+1/(50))^2+` is given by `2500` b. `2550` c. `2450` d. none of these

Explanation

Let n= 50
Let S be the sum of n terms of the given series and `x=1+1/n`. Then,
`S=1+2x+3x^(2)+4x^(2)+….+nx^(n-1)`
`rArrxS=x+2x^(2)+3x^(3)+…+(n-1)x^(n-1)+nx^(n)`
`therefore S-xS=1+[x+x^(2)+..+x^(n-1)]-nx^(n)`
`rArrS(1-x)=(1-x^(n))/(1-x)-nx^(n)`
`rArrS(-1/n)=-n[1-(1+1/n)^(n)]-n(1+1/n)^(n)`
`rArr1/nS=n-n(1+1/n)^(n)+n(1+1/n)^(n)`
`rArr1/nS=n`
`rArrS=n^(2)=(50)^(2)=2500`