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If x + y = 1, prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r)= nx. |
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Answer» SOLUTION :We have `UNDERSET(R=0)OVERSET(n)sumr.^(n)C_(r)X^(r )y^(n-r) =underset(r=1)overset(n)sumn.^(n-1)C_(r-1)x^(r-1)x^(1)y^(n-r)` ` = nx underset(r=1)overset(n)sum .^(n-1)C_(r-1)x^(r-1)y^((n-1)-(r-1))` `= nx(x+y)^(n-1)` ` = nx , [:' x + y = 1]` |
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