If lim (x→1)x+x^2+x^3+...+x^n-n/x-1 = 820,(n∈N) then the value of n is equal to ....

Question

If lim (x→1) \(\frac{x+x^2+x^3+ ...+x^n-n}{x-1}\) = 820,(n∈N) then the value of n is equal to ....

Answer 1

⇒1 + 2 + ..... + n = 820

⇒ n(n + 1) = 2 × 820

⇒n(n + 1) = 40 × 41