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Show that the middle term in the expansi...

Show that the middle term in the expansion of `(x+1)^(2n)` is `(1.3.5.....(2n-1))/(n!) 2^n.x^n`.

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PATHFINDER-BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. Show that the sum of the coefficients of all odd terms in the expansio...

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  2. Find the fifth term form the end in the expansion of (sqrtx/3+2/5x)^11...

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  3. Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.......

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  4. The first three terms in the binomial expansion of (x+y)^n are 1,56 an...

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  5. If n be a positive integer, then by using binomial theorem show that 3...

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  6. Find the greatest value of the term independent of x in the expansion ...

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  7. Find the coefficient of x in the expansion (1-x^2+2x^4)(1-1/x)^6.

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  8. If (1+x+x^2)^n=a0+a1x+a2x^2+.......+a(2n)x^(2n), then prove that a0+a2...

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  9. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

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  10. If the coefficients of four consecutive terms in the expansion of (1+x...

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  11. The 3rd,4th and fifth terms in the expansion of (x+a)^n are 252, 1512,...

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  12. The coefficient of three consecutive terms in the expansion of (1+x)^n...

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  13. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

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  14. Show that the integral part of the value of (9+4sqrt5)^n is odd for po...

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  15. If the 3rd, 4th. 5th and sixth term in the expansion of (x+alpha)^n ar...

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  16. If coefficient of x^2 and x^11 are 27 and -192 respectively of (1+ax+2...

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  17. Find the coefficient of x^5 in the expansion of (1+x)^21+(1+x)^22+...+...

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  18. Determine the x-independent term in the expansion of (1+4x)^p(1+1/(4x)...

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  19. For ninN , 2^(3n)-1 is divisible by

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  20. For ninN , n^3+2n is divisible by

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