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If p and q are positive, then prove that...

If p and q are positive, then prove that the coefficients of `x^p` and `x^q` in the expansion of `(1+x)^(p+q)` will be equal.

Text Solution

Verified by Experts

Given expansion is `(1 + x)^(p + q)`
`:.` Coefficient of `x^(p) = .^(p + q)C_(p)`
and coefficient of `x^(q) = .^(p + q)C_(q)`
`:. (.^(p + q)C_(p))/(.^(p + q)C_(q)) = (.^(p + q)C_(p))/(.^(p + q)C_(p)) = 1 : 1`
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