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Show that coefficient of the middle term of `(1+ x)^(2n)` is equal to the sum of the coefficients of two middle terms of `(1+x)^(2n-1)`.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. Find the middle terms in the expansion of : (x/3+9y)^10.

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  2. Find the middle terms in the expansion of : (x/y+y/x)^(2n+1).

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  3. Show that coefficient of the middle term of (1+ x)^(2n) is equal to th...

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  4. Write and simplify the term involving x^5 in the expansion of (x-1/x)^...

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  5. Determine the term involving x^3 in (5-2x)^6.

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  6. Find the coefficient of x^(10) in the expansion of (2x^(2)-(3)/(x))^(...

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  7. Find the coefficient of the term involving x^10 in the expansion of (x...

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  8. Find the coefficient of the term involving x^2 in the expansion of (3x...

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  9. Find the coefficient of x^5 in (x+ 3)^6.

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  10. Find the coefficient of x^(8) in the expansion of (x^(2) - (1)/(x)...

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  11. Find a positive value of m for which the coefficient of x^2 in the exp...

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  12. Show that coefficient of a^m and a^n in the expansion of (1+a)^(m+n) a...

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  13. Find 'a' if the coefficients of x^(2) and x^(3) in the expanion of (3 ...

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  14. Find the value of r if the coefficients of (2r+4)th and (r - 2) th ter...

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  15. Find the coefficient of a^(5)b^(7) in (a-2b)^(12).

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  16. Find the coefficient of a^4 in the expansion of the product (1+ 2a)^4 ...

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  17. In the binomial expansion (a+b)^n, the coefficients of fourth and thir...

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  18. In the binomial expansion of (1+x)^34, the coefficients of the (2r-1)t...

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  19. Which term is independent of x in the expansion of (2x^2 +1/x)^12 ? An...

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  20. Write and simplify the term independent x in the expansion of (x^2-2/x...

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