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If n is a non zero rational number then...

If n is a non zero rational number then show that
`1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….`

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AAKASH SERIES-BINOMIAL THEOREM-SOLVED EXAMPLES
  1. If x = (1.3)/(3.6) + (1.3.5)/(3.6.9) + (1.3.5.7)/(3.6.9.12) + ….. th...

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  2. If t = 1 - 1/8 + (1.3)/(8.16) -(1.3.5)/(8.16.24) + …… then prove that ...

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  3. If n is a non zero rational number then show that 1 + n/2 + (n (...

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  4. Prove that : Find the 7^("th") term in the expansion of ((4)/(x^(3))+(...

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  5. Prove that : Find the 3^("rd") term from the end in the expansion of (...

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  6. Prove that : Find the coefficient of x^(9) and x^(10) in the expansion...

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  7. Prove that : Find the term independent of x (that is the constant ter...

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  8. Prove that : If the coefficients of (2r+4)^("th") and (r-2)^("nd") te...

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  9. Find the numerically greatest terms in the expansion of (2x +3x)^...

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  10. Find the numerically greatest terms in the expansion of (3x-4y)^(14...

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  11. Prove that : Suppose that n is a natural number and I, F are respecti...

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  12. Prove that : Find the coefficient of x^(6) in (3+2x+x^(2))^(6).

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  13. The term independent of x in the expansion of (1+x+2x^3) (3x^2//2-1//3...

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  14. Find the number of terms free of radical sign in (5^(1//2) +7^(1//5))^...

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  15. Show that the coefficient of x^(k) (0 le k le n) in the expansion of ...

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  16. For natural numbers m, n if (1-y)^m (1+y)^n=1+a1 y +a2 y^2 + …, and a1...

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  17. Prove that : Find the coefficient of x^(6) in (3+2x+x^(2))^(6).

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  18. Find the number of distinct terms in the expansion of (x+(2)/(x)+1)^(2...

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  19. Find the coefficient of a^(5) b^(3)c^(4) in the expansion of (ab+(bc)/...

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  20. Prove that x^n-y^n is divisible by x - y for all positive integers n.

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