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In the binomial expansion of (1+a)^(m+n)...

In the binomial expansion of `(1+a)^(m+n)` , prove that the coefficient of `a^m a n d\ a^n` are equal.

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The correct Answer is:
N/a
`T_(r+1)=^(m+n)C_(r)(1)^(m+n-r).a^(r)`
`=^(m+1)C_(r).a^(r)`
`:.` Coefficient of `a^(m)=^(m+m)C_(m)=(|ul(M+n))/(|ulm.|uln)(" Put "r=m)`
and coefficient of `a^(n)=^(m+n)C_(n)=(|ul(m+n))/(|uln.|ulm)(" Put " r=n)` ltbr. Therefore coefficient of `a^(m)` and coefficient of `a^(n)` are equal.
Hence Proved.
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NAGEEN PRAKASHAN-BINOMIAL THEOREM-Exericse 8.2
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  2. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  3. Find the middle term in the expansion of (3-(x^(3))/(6))^(7)

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  4. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  5. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  6. The coefficient of the (r-1)th, rth and (r+1)th terms in the expansio...

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  7. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  8. Find a positive value of m for which the coefficient of x^2 in the ex...

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  9. Find the coefficient of x^5""in(x+3)^8

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

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  11. Write the general term in the expansion of (x^2-y)^6dot

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  12. Write the general term in the expansion of (x^2-y x)^(12),x!=0

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  13. Find the 4^(t h)term in the expansion of (x-2y)^(12).

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  14. Find the 13^(t h)term in the expansion of (9x-1/(3sqrt(x)))^(18),x!=0

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  15. Find the middle term in the expansion of (3-(x^(3))/(6))^(7)

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  16. Find the middle term in the expansion of :\ (x/3+9y)^(10)

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  17. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  18. The coefficient of the (r-1)th, rth and (r+1)th terms in the expansio...

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  19. prove that the coefficient of x^n in the expansion of (1+x)^(2n) is tw...

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  20. Find a positive value of m for which the coefficient of x^2 in the ex...

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