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Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from `(n+1)^(t h)` to `(2n)^(t h)` term is `1/(r^n)`

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Sum of first n term of G.P.
=`a+a_2+a_3+....+a_n`
=`a+a^r+ar^2+....+ar^(n−1)`
[ ...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. The ratio of the sum of first three terms is to that of first 6 term...

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  2. The 4th and 7th terms of a G.P. are 1/(27)a n d1/(729) respectively. F...

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  3. Show that the ratio of the sum of first n terms of a G.P. to the su...

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  4. If a\ a n d\ b are the roots of x^2-3x+p=0\ a n d\ c ,\ d are the root...

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  5. How many terms of the G.P. 3,3//2,3//4, be taken together to make (30...

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  6. A person has 2 parents, 4 grandparents, 8 great grand parents, and so ...

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  7. A. G.P. consists of an even number of terms. If the sum of all the t...

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  8. Find the sum to infinity of GP -5/4, 5/16,-5/64......

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  9. Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.

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  10. If b=a+a^2+a^3+ dotoo prove that a=b/(1+bdot)

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  11. The first term of G.P. is 2 and the sum to infinity is 6. Find the com...

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  12. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

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  13. Use geometric series to express 0. 555... =0. overline5 as\ a rationa...

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

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

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

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

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

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

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

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