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Let a = lim(n rarr oo) (1+2+3+.....+n)/...

Let ` a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))=`, b = `lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))=` then

A

(1/6)

B

(1/3)

C

(-1)

D

(1/2)

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The correct Answer is:
B
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0, then ...

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  4. If a,b, c, d are positive, then lim(x rarr oo) (1 + 1/(a+bx))^(c+dx)=

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  5. lim(x rarr 0) (a^(x)-b^(x))/x =

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

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  7. lim(x rarr 0) x/(sqrt(x+4)-2) =

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  8. lim(x rarr 0) [[(log(1+x))]/x]=

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  9. lim(x rarr oo)((a^(1/x)+b^(1/x)+c^(1/x))/3)^x, where a, b, c are real ...

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  10. lim(x rarr oo) ((2x+7sinx)/(4x+3cosx)) =

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  11. lim(x rarr 0) (log (1+x))/(3^(x) - 1)=

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  12. lim(theta rarr pi/2) (1-sin theta )/((pi/2 - theta) cos theta)=

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  13. lim(x rarr 0) (x.10^(x)-x)/(1-cos x) =

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  14. lim(x rarr oo) ((x+a)/(x+b))^(x+b) =

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  15. If f(x) = {(2x+b, x lt alpha),(x+d, x gea):} is such that lim(x rarr a...

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  16. The quadratic equation whose roots are l and m, where l = lim(theta ra...

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  17. lim(x rarr 0) (4^(x)-9^(x))/(x*(4^(x)+9^(x)) ) =

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  18. If lim(xtoa)(a^(x)-x^(a))/(x^(x)-a^(a))=-, then :

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  19. lim(x rarr pi/6) ((3sinx - sqrt3 cos x)/(6x-pi)) =

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  20. lim(n rarr oo) 1/n^(3) sum(k=1)^(n) k^(2)x =

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