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Prove that : Find the sum of the infinit...

Prove that : Find the sum of the infinite series
`1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo`

A

`root(3)(3)`

B

`root(4)(4)`

C

`root(4)(8)`

D

`root(3)(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. The coefficient of x^10 in (1-2x + 3x^2)/(1-x) is

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  2. The coefficient of x^9 in the expansion of (1-5x)/(1+x) is

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  3. The coefficient of x^4 in the expansion of ((1 -3x)^2)/((1 - 2x)) is

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  4. For |x| lt 1, the coefficient of x^r in the expansion of ((1+x)^2)/((1...

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  5. If x = 1 + 3a + 6a^2 + 10 a^3 + ……" to " oo terms |a| lt 1, y = 1+4a+1...

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  6. Prove that : If |x| is so small that x^(2) and higher powers of x may ...

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  7. If |x| is so small that all terms containing x^2 and higher powers of ...

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  8. If x = (1*3)/(3*6)+(1*3*5)/(3*6*9)+(1*3*5*7)/(3*6*9*12)+. . . to in...

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  9. 1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

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  10. 1+(1)/(2). (3)/(5) + (1.3)/(2.4) . (9)/(25)+(1.3.5)/(2.4.6).(27)/(125)...

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  11. 1+(1)/(4) + (1.3)/(4.8) + (1.3.5)/(4.8.12)+…...=

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

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  13. 2 + (5)/(2!3) + (5.7)/(3!3^2) + (5.7.9)/(4!3^2) + …..oo =

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  14. Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(...

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  15. Sho that 3/6 + (3.5)/(6.9) + (3.5.7)/(6.9.12)+ ……..oo 3 sqrt3 - 4

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  16. 1 + 1/3 + (1.3)/(1.2) .(1)/(3^2) + (1.3.5.)/(1.2.3).(1)/(3^3) + ……oo =

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  17. Observe the following statements : Statement - I: The total number...

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  18. Let l,m,n are the coefficients of x^5 in (1+2x+3x^2+…..)^(-3//2), (...

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  19. Match the following

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  20. Match the following question

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