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The sum of an infinite geometric series ...

The sum of an infinite geometric series is 15 and the sum of the squares of these terms is 45. Find the series.

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Use geometric series to express 0. 555... = bar0.5 as a rational numb...

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  2. The inventor of the chess board suggested a reward of one grain of whe...

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  3. The sum of an infinite geometric series is 15 and the sum of the sq...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. 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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  20. 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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