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Sum of the n terms of the series 1 . 2^(...

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

A

1)`(1)/(12)[n(n+1)(n+2)(3 n+5)]`

B

2) `(1)/(12)[n(n+1)(n+2)(2 n+5)]`

C

3)` (1)/(12)[n(n+1)(n+2)(n+5)] `

D

4) ` (1)/(12)[n(n+1)(n+2)(2 n+3)]`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
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  2. (1)/(1 . 4 . 7)+(1)/(4 .7 . 10)+(1)/(7 . 10 . 13)+.. . to n terms =

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

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  4. 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 series3+15+35+63+.. ..

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

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

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

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

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

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

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

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

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

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

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

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