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Find the sum to infinity of the series `1^2+2^2x+3^2x^2+oodot`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Find the sum to n terms of the series :1xx2xx3 + 2xx3xx4 + 3xx4xx5 + ....

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  2. If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+......oo...

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  3. Find the sum to infinity of the series 1^2+2^2x+3^2x^2+oodot

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  4. If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-...

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  5. Find the sum of the series 1-3x+5x^2-7x^3+ ton terms.

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  6. In a geometric progression consisting of positive terms, each term ...

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  7. If the A.M. between two numbers exceeds their G.M. by 2 and the GM. ...

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  8. The AM of two given positive numbers is 2. If the larger number is inc...

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  9. Find the sum of the series 1+3x+5x^2+7x^3+..........upto n terms.

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  10. If (a-x)/(p x)=(a-y)/(q y)=(a-z)/(rz) and p ,q ,and r are in A.P., the...

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  11. Find the sum of n terms of the series 1+4/5+7/(5^2)+10/5^3+......

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  12. Find the sum (1^2)/2-(3^2)/(2^2)+(5^2)/(2^3)-(7^2)/(2^4)+....oodot

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  13. If H is the harmonic mean between P and Q then find the value of H//P+...

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  14. If Tr=r(r^2-1), then find sum(r=2)^oo1/Trdot

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  15. Insert four H.M.’s between 2/3 and 2/13.

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  16. If a , b ,a n dc are respectively, the pth, qth , and rth terms of a G...

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  17. The A.M. and H.M. between two numbers are 27 and 12, respectively, t...

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  18. If a ,a1, a2, a3, a(2n),b are in A.P. and a ,g1,g2,g3, ,g(2n),b . are...

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  19. If nine arithmetic means and nine harmonic means are inserted between ...

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  20. If x ,1,a n dz are in A.P. and x ,2,a n dz are in G.P., then prove tha...

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