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The sum of n terms of the series 1^(2)...

The sum of n terms of the series
`1^(2)-2^(2)+3^(2)-4^(2)+5^(2)-6^(2)+...` is

A

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

B

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

C

`-n(n+1)`

D

`n(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
A
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. Sum of the series 1+(3^(2))/(2 !)+(3^(4))/(4 !)+(3^(6))/(6 !)+.. . . t...

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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 n terms of the series 1^(2)-2^(2)+3^(2)-4^(2)+5^(2)-6^(2)...

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  4. Sum of the series S=1^(2)-2^(2)+3^(2)-4^(2)+.. ..-(2002)^(2)+(2003)^...

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  5. If S(n)=(1)/(6) n(n+1)(n+2) is the sum to n terms of a series whose n...

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  6. If S(n)=(1)/(6) n(n+1)(n+2) is the sum to n terms of a series whose n...

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  7. If S(n)=(1)/(6) n(n+1)(n+2) is the sum to n terms of a series whose n...

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  8. Let S(n) denote the sum of the cubes of the first n natural numbers an...

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

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  10. The 10th common term between the series : 3+7+11+"……." and 1+ 6 + 1...

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  11. If the sum of n terms of the series 2^(3)+4^(3)+6^(3)+.. is 3528 , the...

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  12. 1 . 2+2 . 3+3 . 4+.. .. to n terms =

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  13. The 99^(th)term of the series 2+7+14+23+34+.. ..

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  14. If 3+(3+d) (1)/(4)+(3+2 d) (1)/(4^(2)) +.., oo is (44)/(9) thend=

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

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  16. If a(k)=(1)/(k(k+1)) for k=1,2,3, .., n, then (sum(k=1)^(n) a(k))^(...

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  17. If 2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^(2)(n+1)^(2) then k=

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  18. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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  19. If t(n)=(1)/(4)(n+2)(n+3) , n=1,2,3, .. then (1)/(t(1))+(1)/(t(2))...

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  20. sum(k=1)^(5) (1^(3)+2^(3)+.. ..+k^(3))/(1+3+5+.. ..+(2 k-1))=

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