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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 ______.
Options
20.00
30.00
40.00
50.00
MCQ
Fill in the Blanks
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Solution
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
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Concept of Limits
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