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Find the sum to n terms of the series 1^...

Find the sum to n terms of the series `1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+.....`

A

`(n(n+1)^(2)(n+3))/(12)`

B

`(n(n+1)(n+2)^(2))/(12)`

C

`(n(n+1)(n+2))/(12)`

D

`(n(n+1)^(2)(n+2))/(12)`

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Verified by Experts

The correct Answer is:
D
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. The n^(th ) term of the series4+13+28+49+.. . Is

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

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

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

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

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

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

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  8. 1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+.. .. to infty=

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

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  10. (1)/(2 !)+(2)/(3 !)+(3)/(4 !)+.. .. to n terms =

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  11. Sum of 10 terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1+2...

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  12. If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) +...

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  13. Sum of 25 terms of the series 1 . 3+2 . 5+3 . 7+.., is

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  14. If the natural numbers are divided into the groups (1),(2,3),(4,5,6),(...

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  15. If (sum n^(3))(sum n)=(sum n^(2))^(2), then

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  16. 4^(3)+5^(3)+6^(3)+.. .+10^(3)=

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  17. 3+5+7+ …..to n^(th) term is

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  18. ((1)/(2) . (2)/(2))/(1^(3))+((2)/(3) . (3)/(2))/(1^(3)+2^(3)) +((3)/(2...

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  19. The 10^(th ) term of the series 3+13+29+51+79+.. ..

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  20. Sum to 30 terms of 3+4+8+9+13+14+18+19+.. is

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