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Find an infinite G.P. whose first term i...

Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. Find the rational numbers having the following decimal expansion: 3. 5...

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

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

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

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

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  6. 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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  7. 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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  8. 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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  9. 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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  10. 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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  11. If a ,\ b ,\ c are in G.P. prove that loga ,\ logb ,\ logc are in A.P.

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

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

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

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

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  16. The sum of three numbers in G.P. is 56. If we subtract 1,7,21 from the...

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  17. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  18. If a ,\ b\ c are in G.P., prove that the following are also in G.P.: a...

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  19. If a, b, c are in G. P., prove that a^2+ b^2, ab + bc, b^2 +c^2 are al...

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  20. If (a-b),\ (b-c),(c-a) are in G.P. then prove that (a+b+c)^2=3(a b+b c...

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