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

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

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RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. A. G.P. consists of an even number of terms. If the sum of all the ...

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

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

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

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

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

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  7. Use geometric series to express 0. 555... = bar0.5 as a rational numb...

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

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

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

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

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

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

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

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

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

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

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

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

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

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