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Sum to n terms of the series 1+(1+2)+(1+...

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

A

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

B

`(1)/(2)(n^(3)-3 n^(2)+4 n)`

C

`(1)/(5)(n^(3)+3 n^(2)+n)`

D

`(1)/(3)(n^(3)+3 n^(2)-1)`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. 1+3+5+.. . .+(2 n-1)=

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  2. Sum to n terms of 2+4+6+8 ..=

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

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  4. 1 . 3+3 . 5+5 . 7+.. . . to n terms =

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  5. 2 . 4+4 . 6+6 . 8+... to n terms =

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  6. (b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + ...

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  7. 1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =

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

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

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  11. (1)/(1 . 3)+(1)/(3 . 5)+(1) /(5 . 7)+.. to n terms =

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

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

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

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

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

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

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

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

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

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