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(1)/(1 . 4 . 7)+(1)/(4 .7 . 10)+(1)/(7 ....

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

A

`(n(3 n-5))/(8(3 n+1)(3 n+4))`

B

`(n(3 n+2))/(6(3 n+1)(3 n+4))`

C

`(n(3 n+5))/(8(3 n+1)(3 n+4))`

D

none of these

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. (1)/(1 . 3)+(1)/(3 . 5)+(1) /(5 . 7)+.. to n terms =

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

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  3. (1)/(1 . 4 . 7)+(1)/(4 .7 . 10)+(1)/(7 . 10 . 13)+.. . to n terms =

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

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

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

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

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

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

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

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

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

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

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  14. 3+5+7+ …..to n^(th) term is

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

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  16. The sum 1^(2)+1+2^(2)+2+3^(2)+3+..+n^(2)+n is

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  17. Find the sum to n terms of the series 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)...

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  18. sum(n=1)^(n) (1)/((4 n-1)(4 / t+3))=

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  19. If 1+x^(2)=sqrt(3)x, then sum(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

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

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