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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

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The correct Answer is:
D
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 2 (MULTIPLE CHOICE QUESTIONS)
  1. The sum of n terms of the series 1 + (1)/(2) + (1)/(2^(2)) +… is less ...

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  2. The minimum value of n such that 1 + 3 + 3^(2) +...+ 3^(n) gt 1000 is

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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. Let S1 , S2 , …. Be squares such that for each n ge 1 the length of a...

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  5. If A and G be the A .M and G.M between two positive numbers, then the ...

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  6. If the A.M. and G.M. between two numbers are in the ratio m.n., then w...

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  7. If S = (2)/(3) + (8)/(9) + (26)/(27) + (30)/(81)+….+n terms, then the ...

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  8. Sum of n terms of the series (1)/(3) + (5)/(9) + (19)/(27) + (65)/(81)...

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  9. 8 + 88 + 888 +…n terms =

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  10. underset("n digits")((666…6)^(2)) + underset("n digits")((888…8)) is e...

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  11. The value of sum sum(n=1)^(13) ( i^(n) + i^(n+1)) where i= sqrt( -1) ,...

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  12. If |a| lt 1 and |b| lt 1 , then the sum of the series a(a+b) + a^2...

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  13. If S be the sum, P the product and R the sum of the reciprocals of n t...

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  14. If x = 1 + a + a^(2) + a^(3) +…"to" oo (|a| lt 1) and y = 1 b + b^(2) ...

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  15. If x is the first term of a G.P. with infinite number of terms and S(o...

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  16. If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)...

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  17. Given that 0 lt x lt (pi)/(4) and (pi)/(4) lt y lt (pi)/(2) and sum(k ...

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  18. If x = 1 + y + y^(2) + y^(3)+…"to"oo, then y is

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  19. (3)/(4)-(5)/(4^(2))+(3)/(4^(3))-(5)/(4^(4))+(3)/(4^(5))-(5)/(4^(6))+.....

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  20. If {:(x = a + a//r + a//r^(2)+......oo),(y = b - b//r + b//r^(2)-........

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