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Find the sum of the following series to infinity: `1+2//5+3//5^2\ +2//5^3+3//5^4+.....oo`

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. The sum of an infinite geometric series is 15 and the sum of the sq...

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  2. Find the sum of the following series to infinity: 1-1/3+1/(3^2)-1/(3^3...

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  3. Find the sum of the following series to infinity: 1+2//5+3//5^2\ +2//5...

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  4. Find the sum of the following series to infinity: 1/3+1/(5^2)+1/(3^3)+...

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  5. Find the sum of the following series to infinity: 8+4sqrt(2)+4+ddotoo

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  6. Find the sum of the following series to infinity: 10-9+8. 1-7. 29+oo

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  7. Find the value of 9^(1/3). 9^(1/9). 9^(1/27)...up to oo.

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  8. Prove that: 2^(1/4).4^(1/8), 8^(1/16). 16^(1/32)......... oo=2.

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  9. Find the sum off the terms of an infinite decreasing G.P. in which all...

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  10. (b). Express the recurring decimal 0.125125125 ... as a rational numbe...

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  11. Find the rational numbers having the following decimal expansion:\ 0. ...

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  12. Find the rational numbers having the following decimal expansion: 3. 5...

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  13. Find the rational numbers having the following decimal expansion: \ 0....

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  14. Find an infinite G.P. whose first term is 1 and each term is the sum o...

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  15. Show that in an infinite G.P. with common ratio r(|r|<1) , each term b...

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  16. Three numbers whose sum is 15 are in A.P. If they are added by 1,4 and...

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  17. If a ,b ,c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to (a-...

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  18. If a ,\ b ,\ c ,\ d are in G.P., show that: (a b+b c+c d)^2=(a^2+b^2+c...

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  19. If a ,b ,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) ar...

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  20. 29. If a,b,c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, ...

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