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Find the sum of the series 1/(3^2+1)+1/(...

Find the sum of the series `1/(3^2+1)+1/(4^2+2)+1/(5^2+3)+1/(6^2+4)+oo`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find four number in an A.P. whose sum is 20 and sum of their squares i...

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  2. Find the sum of the following series : 0. 7+0. 77+0. 777+ ton term...

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  3. Find the sum of the series 1/(3^2+1)+1/(4^2+2)+1/(5^2+3)+1/(6^2+4)+oo

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  4. Prove that in a sequence of numbers 49,4489,444889,44448889 in which e...

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  5. Find the sum of first 100 terms of the series whose general term is ...

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  6. If the continued product o three numbers in a G.P. is 216 and the sum ...

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  7. Find the sum of the series 2/(1xx2)+5/(2xx3)xx2+(10)/(3xx4)xx2^2+(17)/...

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  8. The sum of some terms of G. P. is 315 whose first term and the comm...

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  9. A sequence of numbers An, n=1,2,3 is defined as follows : A1=1/2 and f...

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  10. The sum of three numbers in GP. is 56. If we subtract 1, 7, 21 from ...

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  11. Find the sum of the products of the ten numbers +-1,+-2,+-3,+-4,a n d+...

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  12. If a, b, c are in A.P., b, c, d are in G.P. and 1/c ,""1/d ,""1/e are ...

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  13. Find the sum sum(r=0) .^(n+r)Cr .

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  14. Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1...

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  15. Write the first five terms of the following sequence and obtain the ...

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  16. Prove that the sum to n terms of the series 11+103+1005+ i s(10/9)(10^...

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  17. If a(n+1)=1/(1-an) for n>=1 and a3=a1. then find the value of (a200...

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  18. Determine the number of terms in a G.P., if a1=3,an=96 ,a n dSn=189.

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  19. Let {an}(ngeq1) be a sequence such that a1=1,a n d3a(n+1)-3an=1 for a...

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  20. Let S be the sum, P the product, and R the sum of reciprocals of n ter...

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