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Find the sum of the infinite series (...

Find the sum of the infinite series
`(7)/(5)(1+(1)/(10^(2))+(1.3)/(1.2).(1)/(10^(4))+(1.3.5)/(1.2.3).(1)/(10^(6))+....)`

A

`root(3)(2)`

B

`sqrt2`

C

`root(3)(3)`

D

`root(3)(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1C (BINOMIAL THEOREM WITH RATIONAL INDEX)
  1. The sum of the series 1+ (2)/(3)((1)/(8)) + (2 xx 5 xx 8)/(3 xx 6 xx 9...

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  2. 1+(k)/(3) + (k(k+1))/(3.6) + (k(k+1) (k+2))/(3.6.9) + …=

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  3. Find the sum of the infinite series (7)/(5)(1+(1)/(10^(2))+(1.3)/(1...

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  4. 1-(1)/(4)+(1.3)/(4.8)-(1.3.5)/(4.8.12)+…..=

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  5. 1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

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  6. 1-(1)/(8)+(1.3)/(8.16)-(1.3.5)/(8.16.24)+…..=

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  7. 1-(3)/(4)+(3.5)/(4.8)-(3.5.7)/(4.8.12)+….=

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  8. 1-(3)/(16)+(1.4)/(1.2)((3)/(16))^2- (1.4.7)/(1.2.3)((3)/(16))^3 + …..=

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  9. If x=(1)/(3)+(1.3)/(3.6)+(1.3.5)/(3.6.9)+…., then x^2+2x-2=

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  10. If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo then find 3x^(2)+6x.

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  11. (1.3)/(3.6)+(1.3.5)/(3.6.9)+(1.3.5.7)/(3.6.9.12)+…=

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  12. (1.4)/(5.10)-(1.4.7)/(5.10.15)+(1.4.7.10)/(5.10.15.20)+….=

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  13. (3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

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  14. (5)/(6.12)+(5.8)/(6.12.18)+(5.8.11)/(6.12.18.24)+…....=

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  15. (5)/(3.6)+(5.7)/(3.6.9)+(5.7.9)/(3.6.9.12)-…....=

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  16. (1)/(4)-(5)/(4.8)+(5.7)/(4.8.12)-…....=

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  17. (3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

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  18. If x=(5)/((2!).3)+(5.7)/((3!).3^(2))+(5.7.9)/((4!).3^(3))+…. then fi...

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  19. If x=1+(3)/(1!)xx(1)/(6)+(3xx7)/(2!)((1)/(6))^(2)+(3xx7xx11)/(3!)((1)/...

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  20. 1+(n)/(2)+(n(n-1))/(2.4)+(n(n-1) (n-2))/(2.4.6)+…....=

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