सिद्ध कीजिए : `n.C(n-1,r-1)=(n-r+1)C(n,r-1)`

.^(n-1)C_(r)+^(n-1)C_(r-1)=

Prove that: (i) r.^(n)C_(r) =(n-r+1).^(n)C_(r-1) (ii) n.^(n-1)C_(r-1) = (n-r+1) .^(n)C_(r-1) (iii) .^(n)C_(r)+ 2.^(n)C_(r-1) +^(n)C_(r-2) =^(n+2)C_(r) (iv) .^(4n)C_(2n): .^(2n)C_(n) = (1.3.5...(4n-1))/({1.3.5..(2n-1)}^(2))

Prove that if 1 le r le n " then " n xx^((n-1))C_(r-1)= (n-r+1).^(n)C_(r-1)

.^((n-1)C_(r) + ^((n-1)) C_((r-1)) is

If 1<=r<=n, then n^(n-1)C_(r)=(n-r+1)^(n)C_(r-1)

If 1lt=rlt=n , then \ n^(n-1)C_r_ _1 =(n-r+1)\ ^n C_(r-1)dot

The result of ^(n-1)C_r+^(n-1)C_(r-1)=

show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

Show that .^(n)C_(r)+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_(r) .

Show that .^nC_r+.^(n-1)C_(r-1)+.^(n-1)C_(r-2)=.^(n+1)C_r