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A sequence of numbers An, n=1,2,3 is def...

A sequence of numbers `A_n, n=1,2,3` is defined as follows : `A_1=1/2` and for each `ngeq2,` `A_n=((2n-3)/(2n))A_(n-1)` , then prove that `sum_(k=1)^n A_k<1,ngeq1`

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Find the sum of the series 2/(1xx2)+5/(2xx3)xx2+(10)/(3xx4)xx2^2+(17)/...

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

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

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

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

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

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  8. 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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  9. Write the first five terms of the following sequence and obtain the ...

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

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  11. If a(n+1)=1/(1-an) for n&gt;=1 and a3=a1. then find the value of (a200...

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

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

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

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  15. If the pth term of an A.P. is q and the qth term is p , then find its ...

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  16. Find the product of three geometric means between 4 and 1/4.

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  17. if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r...

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  18. Insert four G.M.’s between 2 and 486.

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  19. Find the sum 1^2+(1^2+2^2)+(1^2+2^2+3^2)+ up to 22nd term.

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  20. If G is the geometric mean of xa n dy then prove that 1/(G^2-x^2)+1/(G...

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