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Find the sum of the series: (2^(2)+...

Find the sum of the series:
`(2^(2)+4^(2)+6^(2)+8^(2)+ ..."to n terms")`

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The correct Answer is:
`2/3n(n+1)(2n+1)`
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MODERN PUBLICATION-SEQUENCES AND SERIES-VERY SHORT ANSWER TYPE QUESTIONS
  1. Write the next term of the sequence: 1/6,1/3,1/2……..

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  2. Which term in the A.P. 68,64,60 is -8?

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  3. Find the A.M. between: (i) 3.7 and 5.5 (ii) 6 and -8

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  4. (i) Find the 10 th term of the G.P. 5,25,125…………….. (ii) Find the ...

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  5. Which term of the following sequences:(a) 2,2sqrt(2),4,. . . is 128? (...

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  6. Find the indicated term of the following G.P.: 12, 8, 16/3, …………..t...

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  7. In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th t...

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  8. Evaluate sum(n=1)^(13)(i^n+i^(n+1)), where n in Ndot

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  9. Given a G.P. with a=1,r=sqrt(2). Find S(20) ??

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  10. Find the sum of the infinite geometric series (1+1/3+1/9+1/27+...oo).

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  11. Find the sum of series in GP 1/3, 1/9, 1/27……………….. up tooo

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  12. 0.3,0.18,0.108,………….to oo

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  13. Find the sum of the following series: (sqrt(2)-1)+1+(sqrt(2)-1)+oo

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  14. Find the sum of the following series to infinity: 2//5+3//5^2\ +2//5^3...

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  15. Find a rational number for the following which will have as its expant...

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  16. Find the sum to inifinity of the following series: 1+2/3+3/(3^(2))+4...

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  17. Find the sum of the series: (2^(2)+4^(2)+6^(2)+8^(2)+ ..."to n te...

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  18. Sum of n terms of the following series1^3+3^3+5^3+7^3+

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  19. 1.3+3.5+5.7+..... n terms =

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  20. Find the sum of first n terms of the series whose nth term is 3n^(2)+5...

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