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If first three terms of the sequence 1/1...

If first three terms of the sequence `1/16 ,a , b , 1/6` are in geometric series and last three terms are in harmonic series, then find the values of `a , bdot`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If a ,b ,a n dc be in G.P. and a+x ,b+x ,and c+x in H.P. then find the...

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  2. The ratio of the sum of m and n terms of an A.P. is m^(2) :n^(2). Show...

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  3. If first three terms of the sequence 1/16 ,a , b , 1/6 are in geometri...

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  4. The sum of n ,2n ,3n terms of an A.P. are S1S2, S3, respectively. Prov...

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  5. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th ...

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  6. If x is a positive real number different from 1, then prove that the n...

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  7. Which term of the sequence 20 ,19 1/4, 18 1/2, 17 3/4,dot is the first...

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  8. If Sn=n P+(n(n-1))/2Q ,w h e r eSn denotes the sum of the first n term...

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  9. Find the sum sum(r=1)^n r(r+1)(r+2)(r+3)

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  10. Find the sum sum(r=1)^n r/((r+1)!) where n!=1xx2xx3....n.

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  11. Find the sum sum(r=1)^n r(r+1)(r+2)(r+3)

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  12. Find the sum 1+1/(1+2)+1/(1+2+3)+..........+1/(1+2+3+.........+n)dot

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  13. Find the sum to n terms of the series 1/(1 + 1^2 + 1^4) + 2/(1 + 2^2...

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  14. Find the sum to n terms of the series 3//(1^2xx2^2)+5//(2^2xx3^2)+7//(...

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  15. Find the sum sum(r=1)^n1/((a r+b)(a r+a+b))dot

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  16. If x=sum(n=0)^ooa^n , y=sum(n=0)^oob^n , z=sum(n=0)^ooc^n , w h e r e ...

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  17. If the sum of the series sum(n=0)^oor^n ,|r|<1 is s , then find the s...

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  18. Find the sum of the series sum(k=1)^(360)(1/(ksqrt(k+1)+(k+1)sqrt(k)))

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  19. Find the sum (1^4)/(1xx3)+(2^4)/(3xx5)+(3^4)/(5xx7)+......+(n^4)/((2n-...

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  20. Find the value of 11^2+12^2+13^2++20^2dot

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