1.

यदि `C_(r),""^(n)C_(r)` को सूचित करें तो साबित कीजिए कि `(C_(1))/(C_(0))+2.(C_(2))/(C_(1))+3.(C_(3))/(C_(2))+...+n.(C_(n))/(C_(n-1))=(n(n+1))/(2)`

Answer» `t_(r)"(r वाँ पद)"=r.(""^(n)C_(r))/(""^(n)C_(r-1))`
`=r(n!)/(r!(n-r)!).((r-1)!(n-r+1)!)/(n!)=n-r+1`
L.H.S.`=t_(1)+t_(2)+...+t_(n)=n+(n-1)+(n-2)+...+1=(n(n+1))/(n)`


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