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If each term of an infinite G.P. is twic...

If each term of an infinite G.P. is twice the sum of the terms following it, then find the common ratio of the G.P.

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. 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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  2. Find the sum 1+4+13+40+121+dot

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

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

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

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  7. 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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  8. If the sum of the squares of the first n natural numbers exceeds theri...

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  9. If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N suc...

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  10. If sum(r=1)^n tr=n/8(n+1)(n+2)(n+3), then find sum(r=1)^n1/(tr)dot

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

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

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

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

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

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

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  18. The AM of teo given positive numbers is 2. If the larger number is inc...

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

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  20. 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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