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lim(n rarr oo) 1/n^(3) { 1+3+6+...+ (n(n...

`lim_(n rarr oo) 1/n^(3) { 1+3+6+...+ (n(n+1))/2} =`

A

(-1/6)

B

(1/5)

C

(1/6)

D

(1/4)

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. lim(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) ...

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  3. lim(n rarr oo) 1/n^(3) { 1+3+6+...+ (n(n+1))/2} =

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  4. If S(n) = (1)/(1.4)+(1)/(4.7) + (1)/(7.10) +……. to n terms, then lim(n...

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  5. lim(x rarr 1) (x^(2)-1)/(|x-1|) =

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  6. If f(x) = {(1/(1+e^(1/x)), x ne 0),(0, x= 0):} then f(x) is

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  7. The right hand and left hand limit of the function f(x)={{:((e^(1//x)-...

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  8. Let f(x) = {(x", if x is irrational"),(0", if x is ratinal"):} then f ...

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  9. f(x) = (x^(3)+x^(2)-16x+20)/(x-2)^2, x ne 2. The value which should be...

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  10. Let f(x) = (tan ((pi)/(4) - x))/(cot 2 x), x ne pi//4, the value which...

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  11. For what value the function f(x) = (3x+4tanx)/x at x = 0 is continuous

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  12. If f(x) = x . (sin)1/x, x ne 0, then the value of the function at x = ...

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  13. The function f(x)=|x|+(|x|)/(x) is

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  14. Consider f(x)={{:((x^(2))/(|x|)","x!=0),(0","x=0.):}

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  15. The value of f(2) so that f(x) = (2^(x+2)-16)/(4^(x)-16) is continuous...

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  16. If f(x) = {((|x-1|)/(x-1), x ne 1), (0, x = 1):} then the correct stat...

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  17. The function y = 3sqrtx-|x-1| is continuous at

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  18. Let f(x) = (sqrt(1 + sin x)-sqrt(1-sin x))/(x)lim The value, which sho...

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  19. To make f(x)=(x+1)^(cotx) continuous at x=0,f(0) must defined as

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  20. if f(x) = 1/(1-x) (x ne 1), {f[f(x)]} is

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