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The value of 1-1/2(2/3)+1/3(2/3)^(2)-1/4...

The value of `1-1/2(2/3)+1/3(2/3)^(2)-1/4(2/3)^(3)+...` is

A

`log(5/3)`

B

`3/2log(5/3)`

C

`5/3log(5/3)`

D

`2/3log(2/3)`

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SURA PUBLICATION-BINOMIAL THEOREM, SEQUENCES AND SERIES-EXERCISE 5.5
  1. The value of 2 + 4 + 6 + ….+ 2n is

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  2. The coefficient of x^(6) in (2+2x)^(10) is

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  3. The coefficient of x^(8)y^(12) in the expansion of (2x+3y)^(20) is

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  4. If ""^(n)C(10)gt""^(n)C(r) for all possible r, then a value of n is

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  5. If a is the arithmetic mean and g is the geometric mean of two numbers...

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  6. If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then...

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  7. The sequence 1/sqrt3,1/(sqrt3+sqrt2),1/(sqrt3+2sqrt2),... form an

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  8. The HM of two positive numbers whose AM and GM are 16, 8 respectively ...

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  9. If S(n) denotes the sum of n terms of an AP whose common difference is...

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  10. The remainder when 38^(15) is divided by 13 is

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  11. The n^(th) term of the sequence 1, 2, 4, 7, 11, … is

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  12. The sum up to n terms of the series 1/(sqrt1+sqrt3)+1/(sqrt3+sqrt5)+1/...

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  13. The n^(th) term of the sequence 1/2,3/4,7/8,15/16,... is

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  14. Sum of first 'n' terms of the series sqrt(2)+sqrt(8)+sqrt(18)+… is .

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  15. The value of the series 1/2+7/4+13/8+19/16+... is

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  16. The sum of an infinite GP is 18. If the first term is 6, the common ra...

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  17. The coefficient of x^(5) in the series e^(-2x) is

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  18. The value of 1/(2!)+1/(4!)+1/(6!)+... is

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  19. The value of 1-1/2(2/3)+1/3(2/3)^(2)-1/4(2/3)^(3)+... is

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