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1/2+3/4+7/8+15/16+..... t o n terms =...

`1/2+3/4+7/8+15/16+..... t o` n terms =

A

`2^n-1`

B

`2n-n-1`

C

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

D

none of these

Text Solution

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The correct Answer is:
C
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

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  2. The sum of integer in between 1 to 100 which is divisible by 2 or 5 is

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  3. 1/2+3/4+7/8+15/16+..... t o n terms =

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  4. 0ltthetaltpi/2, if x=sum(n=0)^inftycos^(2n)theta,y=sum(n=0)^inftysin^(...

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  5. If x in{1,2,3......9} and fn(x) =x x x ...x (n digits ), then fn^2(3)+...

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  6. Four no. are in AP . If their sum is 20 and the sum of their squares i...

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  7. Sum of n terms of series 1.3+3.5+5.7+....is

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  8. If the sum of an infinitely decreasing GP is 3, and the sum of the squ...

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  9. 1+2.2+3.2^2+4.2^3+....100.2^99 equals

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  10. If A1,A2 be two AM's and G1,G2 be the two GM's between two number a an...

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  11. If H1,H2,H3,.......Hn be n harmonic means between a and b then (H1+a)...

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  12. If a,b,c are in AP and a^2,b^2,c^2 are in HP, then

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  13. If between 1 and 1/31 there are n H.M's and ratio of 7th and (n-1)^th ...

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  14. (a^(n+1)+b^(n+1))/(a^n+b^n) is AM/GM/HM, between a and b if n is equal...

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  15. Sum of infinite terms of series 3+5. 1/4+7. 1/4^2+..... is

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  16. The value of x for which 1/(1+sqrtx),1/(1-x),1/(1-sqrtx) are in AP li...

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  17. If the non-zero numbers a,b,c are in AP and tan^-1a,tan^-1b,tan^-1c ar...

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  18. If a,b,c,d are distinct positive numbers in AP, then

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  19. If sum(r=1)^nr(r+1)(2r+3)=an^4+bn^3+cn^2+dn+e, then

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  20. The pth term Tp of HP is q(p+q) and qth term Tq is p(p+q) when pgt1,qg...

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