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In the expansion of (1+x+x^2+x^3+…..oo)^...

In the expansion of `(1+x+x^2+x^3+…..oo)^3, ` coefficient of `x^3` is

A

4

B

6

C

8

D

10

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. For |x| lt 1, the (r + 1)^(th) term in the expansion of sqrt(1 - x) is

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  2. The general term of (2a - 3b)^(-1//2) is

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  3. In the expansion of (1+x+x^2+x^3+…..oo)^3, coefficient of x^3 is

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  4. In the expansion of (1-2x+3x^2 -4x^3+…."to")^4 coefficient of x^2 is

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  5. The coefficient of x^24 in (1+3x+6x^2 + 10x^3 + ……oo)^(2//3) is

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  6. The coefficient of x^10 in (1-2x + 3x^2)/(1-x) is

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

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

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

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

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

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

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  13. 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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  14. 1-(1)/(5)+(1.4)/(5.10) - (1.5.7)/(5.10.15)+…..=

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  15. 1+(1)/(2). (3)/(5) + (1.3)/(2.4) . (9)/(25)+(1.3.5)/(2.4.6).(27)/(125)...

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  16. 1+(1)/(4) + (1.3)/(4.8) + (1.3.5)/(4.8.12)+…...=

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

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  18. 2 + (5)/(2!3) + (5.7)/(3!3^2) + (5.7.9)/(4!3^2) + …..oo =

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

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

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