Question

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 ______.

पर्याय

• 20.00

• 30.00

• 40.00

• 50.00

Answer 1

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 40.00.

Explanation:

`lim_(x -> 1) ((x - 1))/(x - 1) + ((x^2 - 1))/(x - 1) + ...... + ((x^n - 1))/(x - 1)` = 820

⇒ 1 + 2 + 3 + ........ + n = 820

⇒ `sumn` = 820

⇒ `(n(n + 1))/2` = 820

⇒ n = 40