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The sum of 0. 2+0004+0. 00006+0. 0000008...

The sum of `0. 2+0004+0. 00006+0. 0000008+...` to `oo` is `(200)/(891)` b. `(2000)/(9801)` c. `(1000)/(9801)` d. none of these

A

`(200)/(891)`

B

`(2000)/(9801)`

C

`(1000)/(9801)`

D

none

Text Solution

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The correct Answer is:
B
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ML KHANNA-PROGRESSIONS -PROBLEM SET - 4 (MULTIPLE CHOICE QUESTIONS)
  1. The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omeg...

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  2. For and odd integer n ge 1, n^(3) - (n - 1)^(3) + …… + (- 1)^(n-1) ...

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  3. The sum of the series (1)/(3.5) + (1)/(5.7) + (1)/(7.9)+…. ad infinity...

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  4. If Sigma(r=1)^(n)t(r)=(1)/(6)n(n+1)(n+2), AA n ge 1, then the value o...

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  5. The sum of the infinite series 1 + (1+a) x + (1 + a + a^(2)) x^(2) + (...

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  6. Sum of the series 1 + 2 + 4 + 7 +…+ 67 is equal to

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  7. 99^(th) term of the series 2 + 7 + 14 + 23 + 34 +…is

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  8. Find the 50th term of the series 2+3+6+11+18+….

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  9. Let P = 3^(1//3). 3^(2//9) . 3^(3//27)…oo, then P^(1//3) is equal to

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  10. 2^(1//4).4^(1//8).8^(1//16).16^(1//32)…. is equal to

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  11. If 3 + (1)/(4) (3 + d) + (1)/(4^(2)) (3 + 2d)+…oo = 8, then the value ...

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  12. The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ ....

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  13. The sum to infinite terms of the arithmetic - gemoetric progression 3,...

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  14. The sum o f series 1+4/5+7/(5^2)+(10)/(5^3)+oo is 7//16 b. 5//16 c. ...

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  15. The sum to infinity of the series 1 + (2)/(3) + (6)/(3^(2)) + (10)/(3^...

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  16. The sum of 0. 2+0004+0. 00006+0. 0000008+... to oo is (200)/(891) b. ...

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  17. The sum of the first n terms of the series (1)/(2)+(3)/(4)+(7)/(8)+(15...

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  18. Sum of the series 1 + 3 + 7 + 15 + 31 +… to n terms is

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  19. Sum of the series 1 + 2.2 + 3.2^(2) + 4.2^(3)+…+ 100.2^(99) is

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  20. The positive numbers are written in a triangular array as shown. {:(...

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