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Show that x^(n) =1 + n(1 -1/x) + (n(n+1)...

Show that `x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...`

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PREMIERS PUBLISHERS-BINOMIAL THEOREMN,SEQUENCES AND SERIES -PROBLEMS FOR PRACTICE(Choose the correct option for the following)
  1. Show that x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...

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  2. The sum upto n terms of the series sqrt(3) + sqrt(12) + sqrt(27) + sqr...

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  3. The sum up to n terms of the series 1/(sqrt(1) + sqrt(3)) + 1/(sqrt(3)...

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  4. The remainder when (52)^(15) is divided by 17 is

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  5. If HM and GM of two numbers are 10/9 and 3, then its AM is :

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  6. The no. of terms in the expansion (a+b)^(100)

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  7. Find the term independent of x in the expansion of (x^(2) - 1/x)^(7)

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  8. The coefficient of x^(4) in the expansion of (x/2-3/x^(2))^(10) is

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  9. If S(n) denotes the sum of n terms of an AP whose first term is a, com...

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  10. The coefficient of x^(5) in the expansion of (e^(x) + e^(-x)) is:

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  11. 2[1/2 + 1/(3.2^(3)) + 1/(5.2^(5)) + …]is :

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  12. match the following

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  13. match the following

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  14. Find the odd man out: For any two positive integers:

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  15. AM, GM, HM denote the arithmetic, geometric and harmonic means of a an...

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  16. Find the odd man out in the following:

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  17. Find the correct statement:

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  18. Find the correct statement:

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  19. Find the incorrect statement:

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  20. Assertion (A): In the expansion of (a +b)^(n) n in N the coefficient a...

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  21. Assertion: If a and b are distinct integers then (a - b) is a factor ...

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