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The n^(th) term of the sequence 1/2,3/4,...

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

A

`2^(n)-n-1`

B

`1-2^(-n)`

C

`2^(-n)+n-1`

D

`2^(n-1)`

Text Solution

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The correct Answer is:
B
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FULL MARKS-BINOMIAL THEOREM, SEQUENCES AND SERIES -EXERCISE 5.5
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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 (1+x^(2))^(2)(1+x)^(n)=a(0)+a(1)x+a(2)x^(2)+…..+x^(n+4) and if a(0)...

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  7. 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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  8. The sequence (1)/(sqrt(3)),(1)/(sqrt(3)+sqrt(2)),(1)/(sqrt(3)+2sqrt(2)...

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

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

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

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

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  13. The sum up to n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)...

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

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  15. The sum upto n terms of the series sqrt(3) + sqrt(12) + sqrt(27) + sqr...

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

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

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

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

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

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