1.

If x + y = 1, prove that sum_(r=0)^(n) r""^(n)C_(r) x^(r ) y^(n-r)= nx.

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]`


Discussion

No Comment Found

Related InterviewSolutions