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If b=a+a^2+a^3+ dotoo prove that a=b/(...

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

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Given,`b=a+a^2+a^3+ `
Now,`a+a^2+a^3+ ` is G.P so
first term is =`a`
Common ratio=`a`
Sum of infinite series=`a/(1-r)`
`=a/(1-a)`
Comparing with original equation `b=a+a^2+a^3+ `
we get ...
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RD SHARMA-GEOMETRIC PROGRESSIONS-Solved Examples And Exercises
  1. Find the sum to infinity of GP -5/4, 5/16,-5/64......

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. The terms of an infinitely decreasing G.P. in which all the terms are ...

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  17. Express the recurring decimal 0.125125125 ... as a rational number.

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

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  19. Find the rational numbers shaving the following decimal expansion: 3. ...

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

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