Question

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

Options

• 20.00

• 30.00

• 40.00

• 50.00

Answer 1

If ${\displaystyle \underset{x\to 1}{lim}\frac{x+x^2+x^3\mid +....+x^n-n}{x-1}}$ = 820, (n ∈ N) then the value of n is equal to 40.00.

Explanation:

${\displaystyle \underset{x\to 1}{lim}\frac{(x-1)}{x-1}+\frac{(x^2-1)}{x-1}+......+\frac{(x^n-1)}{x-1}}$ = 820

⇒ 1 + 2 + 3 + ........ + n = 820

⇒ ${\displaystyle \sum n}$ = 820

⇒ ${\displaystyle \frac{n(n+1)}{2}}$ = 820

⇒ n = 40