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If `S` denotes the sum to infinity and `S_n` the sum of `n` terms of the series `1+1/2+1/4+1/8+ ,` such that `S-S_n<1/(1000),` then the least value of `n` is `8` b. `9` c. `10` d. 11

A

8

B

9

C

10

D

11

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Exercise
  1. If the pth, qth, and rth terms of an A.P. are in G.P., then the common...

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  2. If log2,log(2^x-1)a n dlog2log(2^x+3) are in A.P., write the value of ...

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  3. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

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  4. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

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  5. a, b, c are sides of a triangle and a, b, c are in GP If log a- log ...

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  6. about to only mathematics

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  7. If x^(a)=x^(b//2)z^(b//2)=z^(c), then a,b,c are in

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  8. A G.P. consists of an even number of terms. If the sum of all the t...

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  9. The interior angles of a polygon are in A.P. the smallest angle is 120...

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  10. For what value of b, will the roots of the equation cos x=b, -1legle1 ...

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  11. about to only mathematics

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  12. Find the sum of the series 1+(4)/(5)+(7)/(5^(2))+(10)/(5^(3))+"....." ...

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  13. about to only mathematics

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  14. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  15. Find the sum 1+(1+2)+(1+2+2^(2))+(1+2+2^(2)+2^(3))+ …. To n terms.

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  16. If a,b,c are in H.P., then the value of ((1)/(b)+(1)/(c)-(1)/(a))((1...

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  17. The 5th term of the series (10)/(9),(1)/(3)sqrt((20)/(3)),(2)/(3),… is

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  18. If x^(18)=y^(21)=z^(28), then 3,3 log(y)x,3log(z)y,7log(x)z are in

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  19. If d,e,f are G.P. and the two quadratic equations ax^(2)+2bx+c=0andd...

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  20. The sum of n terms of the following series 1+(1+x)+(1+x+x^2)+.... will...

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