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The limit of sum(n=1)^(1000)(-1)^(n)x^(n...

The limit of `sum_(n=1)^(1000)(-1)^(n)x^(n)` as `x rarroo`

A

does not exist

B

exists and equals to 0

C

exists and approaches `+oo`

D

exists and approaches `-oo`

Text Solution

Verified by Experts

The correct Answer is:
C
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MTG-WBJEE-LIMITS AND CONTINUITY-WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 1 : SINGLE OPTION CORRECT TYPE)
  1. The limit of [(1)/(x)sqrt(1+x)-sqrt(1+(1)/(x^(2))]] as x rarr0

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  2. The limit of x sin (e^(-1//x)) as x rarr0

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  3. The limit of sum(n=1)^(1000)(-1)^(n)x^(n) as x rarroo

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  4. The function f(x)=(tan{pi[x-(pi)/(2)]})/(2+[x]^(2)), where [x] denotes...

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  5. LEt f(x) be a differentiable function and f'(4)=5. Then, lim(x->2)(f(4...

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  6. If lim(xrarr0)(2a sin x-sin 2x)/(tan^(3)x) exists and is equal to 1, t...

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  7. Let [x] denote the greatest integer less than or equal to x for any re...

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  8. If lim(xrarr0)(axe^(x)-b log(1+x))/(x^(2))=3, then the value of a and ...

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  9. Let f : R -> R be defined as f(x)={0, x is irrational sin|x|, x is ...

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  10. Let x(n)=(1-(1)/(3))^(2)(1-(1)/(6))^(2)(1-(1)/(10))^(2)…(1-(1)/((n(n+1...

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  11. Let [x] denote the greatest integer less than or equal to x. Then the ...

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  12. Let f:[-2, 2]rarrR be a continuous function such that f(x) assumes onl...

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  13. lim(x rarr 1)((1+x)/(2+x))^((1-sqrt(x))/(1-x))

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  14. the value of lim(n->oo) {sqrt(n+1)+sqrt(n+2)+...........+sqrt(2n-1)}/n...

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  15. If f''(x)=k,k != 0 , then the value of lim(x->0)(2f(x)-3f(2x)+f(4x))...

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  16. lim(xrarr0)(sinx)^(2tanx)

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  17. The value of lim(n->oo)[n/(n^2+1^2)+n/(n^2+2^2)++1/(2n)] is

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  18. f(x) = 3x^10 – 7x^8+ 5x^6 -21x^3 + 3x^2 –7, then is the value of lim(...

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  19. Let f:[a, b] rarrR be such that f is differentiable in (a, b), f is co...

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  20. lim(xrarr0^(+))(x^(n)lnx), n gt0

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