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If G is the geometric mean of xa n dy th...

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

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. Insert four G.M.’s between 2 and 486.

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

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

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  4. If the A.M. of two positive numbers aa n db(a > b) is twice their geom...

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  5. The sum of infinite number of terms in G.P. is 20 and the sum of their...

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  6. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+....+n(1-x)(1-2x) ...

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  7. Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.

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  8. Three numbers are in G.P. whose sum is 70. If the extremes be each mul...

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  9. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+o...

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  10. Find the sum of n terms 1+4+13+40+121+....dot

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  11. If each term of an infinite G.P. is twice the sum of the terms foll...

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  12. The sum to n terms of series 1+(1+1/2+1/(2^2))+(1+1/2+1/(2^2)+1/(2^3))...

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  13. Find the sum of the following series: (sqrt(2)+1)+1+(sqrt(2)-1)+.........

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  14. If the set of natural numbers is partitioned into subsets S1={1},S2={2...

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  15. If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1)) is a polomial in x ,...

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  16. If the sum of the squares of the first n natural numbers exceeds their...

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  17. If f(x) is a function satisfying f(x+y)=f(x)f(y) for all x,yin N such ...

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  18. If sum(r=1)^nTr =n/8(n+1)(n+2)(n+3) then find sum(r=1)^n1/Tr

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  19. Find the sum to n terms of the series :1xx2xx3 + 2xx3xx4 + 3xx4xx5 + ....

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

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