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Find the sum (1^2)/2-(3^2)/(2^2)+(5^2)/(...

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

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then...

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

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

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  4. If H is the harmonic mean between Pa n dQ then find the value of H//P+...

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

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

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

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  8. The A.M. and H.M. between two numbers are 27 and 122, respectively, ...

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  9. 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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  10. If nine arithmetic means and nine harmonic means are inserted between ...

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  11. 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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  12. Find two numbers whose arithmetic mean is 34 and the geometric mean is...

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  13. If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p...

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  14. If A.M. and G.M. between two numbers is in the ratio m : n then prove...

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  15. Prove that (666....6)^2+(888....8)=4444.....4.

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  16. If a is the A.M. of b and c and the two geometric mean are G1 and ...

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  17. If a ,b ,c ,d are distinct integers in an A.P. such that d=a^2+b^2+c^2...

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  18. The 8th and 14th term of a H.P. are 1/2 and 1/3, respectively. Find it...

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  19. Find the number of common terms to the two sequences 17,21,25,...,417 ...

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  20. If the 20th term of a H.P. is 1 and the 30th  term is -1/17, then find...

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