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1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+....

 `1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+..` . to `n` terms =

A

` (1)/(3)[n(n+2)]`

B

`(1)/(4)[n(n+3)]`

C

`(1)/(5)[n(n+4)]`

D

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

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
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  3. 1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =

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  7. (1)/(1 . 3)+(1)/(3 . 5)+(1) /(5 . 7)+.. to n terms =

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

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  9. (1)/(1 . 4 . 7)+(1)/(4 .7 . 10)+(1)/(7 . 10 . 13)+.. . to n terms =

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  10. Sum of the n terms of the series 1 . 2^(2)+2 . 3^(2)+3 . 4^(2)+..

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  11. If t(n) denotes the nth term of the series : 2+3+6+11+18+"………." , th...

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  18. Sum of 25 terms of the series 1+2 . 2+3 . 2^(2)+4 . 2^(3)+5 . 2^(4)+...

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  20. 3+5+7+ …..to n^(th) term is

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