Lt (x tending to zero)(x+x^2+x^3+.....+x^n-n)/(x-1)

Lt(x tends to 0)(x+x^2+x^3+..........+x^n-n)/x-1=Lt(x tends to 0)(x-1+x^2-1^2+x^3-1^3+..........+x^n-1^n)/x-1Then separate the denominator, we get1+2*1+3*1^2+........... +n*1^n-1As Lt(x tends to 0)(x^n-a^n)/x-a=n*a^n-1Therefore we get,1+2+3+........+nWhich is equal to n(n+1)/2

Approved