सिद्ध कीजिए कि
`.^(2n)C_(n)+^(2n)C_(n-1) = 1/2*^(2n+2)C_(n+1)`

Explanation

`L.H.S = ^(2n)C_(n) + ^(2n)C_(n-1)`
` = ^(2n+1)C_(n) " "(.:'^(n)C_(r) +^(n)C_(r-1) = ^(n+1)C_(r))`
` = ^(2n+1)C_(n)`
` = ((2n+1)!)/(n!(2n+1-n)!)`
` = ((2n+2)(2n+1)!)/((2n+2)*n!*(n+1)!) `
` = ((2n+2)!)/(2*(n+1)*n!(n+1)!)`
` = 1/2 * ((2n+2)!)/((n+1)!*(n+1)!)`
` = 1/2 *^(2n+2)C_(n+1) = R.H.S`