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Let S(k) =sum( i =0) ^(oo) (1)/((k +1)^(...

Let `S_(k) =sum_( i =0) ^(oo) (1)/((k +1)^(t)),` then `sum _(k =1) ^(n) kS_(k)` equal :

A

`(n (n +1))/(2)`

B

`(n (n -1))/(2)`

C

`(n (n +2))/(2)`

D

`(n (n +3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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VK JAISWAL ENGLISH-SEQUENCE AND SERIES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let S(k) =sum( i =0) ^(oo) (1)/((k +1)^(t)), then sum (k =1) ^(n) kS(...

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  2. Let a,b,c,d be four distinct real number in A.P.Then the smallest posi...

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  3. The sum of all digits of n for which sum (r =1) ^(n ) r 2 ^(r ) = 2+2^...

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  4. If lim ( x to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =

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  6. Three distinct non-zero real numbers form an A.P. and the squares of t...

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  7. which term of an AP is zero -48,-46,-44.......?

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  8. In an increasing sequence of four positive integers, the first 3 terms...

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  9. The limit of (1)/(n ^(4)) sum (k =1) ^(n) k (k +2) (k +4) as n to oo i...

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  10. Which is the last digit of 1+2+3+……+ n if the last digit of 1 ^(3) + ...

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  11. There distinct positive numbers, a,b,c are in G.P. while log (c) a, lo...

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  13. If sum ( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relativel...

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  15. A cricketer has to score 4500 runs. Let a (n) denotes the number of ru...

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  17. Let f (n)=(4n + sqrt(4n ^(2) -1))/( sqrt(2n +1 )+sqrt(2n-1)),n in N th...

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  18. Find the sum of series 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+…… oo, where the...

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  19. Let a (1), a(2), a(3),…….., a(n) be real numbers in arithmatic progres...

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  20. Let the roots of the equation 24 x ^(3) -14x ^(2) + kx +3=0 form a geo...

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  21. How many ordered pair (s) satisfy log (x ^(3) + (1)/(3) y ^(3) + (1)/(...

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