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Find the sum off the terms of an infinit...

Find the sum off the terms of an infinite decreasing G.P. in which all the terms are positive, the first term is 4, and the difference between the third and fifth term is equal to 32/81.

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Find the value of 9^(1/3). 9^(1/9). 9^(1/27)...up to oo.

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

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

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

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

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

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

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

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

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

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  11. 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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  12. 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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  13. 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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  14. 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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  15. If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A...

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  16. If a ,\ b ,\ c are in G.P. prove that loga ,\ logb ,\ logc are in A.P.

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  17. If a ,\ b ,\ c are in G.P. prove that 1/((log)a m),1/((log)b m),1/((lo...

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  18. Find k such that k+9,\ k-6 and 4 form three consecutive terms of a G.P...

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  19. Three numbers are in A.P. and their sum is 15. If 1,3,9 be added to ...

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  20. The sum of three numbers which are consecutive terms of an A.P. is 21....

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