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The sum of first 9 terms of the serie...

The sum of first 9 terms of the series :
`1^3/1+(1^3+2^3)/(1+3)+(1^3+2^3+3^3)/(1+3+5)+....` is :

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. (b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + ...

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

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  3. The sum of first 9 terms of the series : 1^3/1+(1^3+2^3)/(1+3)+(1...

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  4. The sum of (1^(3))/(1)+(1^(3)+2^(3))/(1+2)+ (1^(3)+2^(3)+3^(3))/(1+2+3...

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  5. Sum to n terms of the series (1)/(2 . 5) +(1)/(5 . 8)+(1)/(8 . 11)+..=

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  6. (1)/(1 . 3)+(1)/(3 . 5)+(1) /(5 . 7)+.. to n terms =

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

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  8. (1)/(1 . 4 . 7)+(1)/(4 .7 . 10)+(1)/(7 . 10 . 13)+.. . to n terms =

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

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

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  11. Sum to n terms of the series1+3+7+13+.. .=

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  12. Sum to n terms of the series3+15+35+63+.. ..

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  13. The n^(th ) term of the series 1+5+12+22+35+.. ..

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  14. Sum to n terms of the series2+6+12+20+.. is,

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  15. Sum of n terms of the series 1+2 x+3 x^(2)+4 x^(3)+..,(x ne 1) is

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  16. Sum of 25 terms of the series 1+(2)/(2)+(3)/(2^(2))+(4)/(2^(3))+.. ....

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

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  18. The n^(th ) term of the series 1+4+13+40+.. .is

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  19. 3+5+7+ …..to n^(th) term is

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  20. The n^(th ) term of the series4+13+28+49+.. . Is

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