Prove that `.^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3)` if `n gt 7`.

Explanation

We have, `.^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) " "[because.^(n)C_(r)+.^(n)C_(r-1)=.^(n+1)C_(r)]`
`hArr .^(n)C_(4)gt.^(n)C_(3)`
`hArr (n!)/(4!(n-4)!)gt(n!)/(3!(n-3)!)`
`hArr (1)/(4(n-4)!)gt(1)/((n-3)(n-4)!)" "[becausem!=m(m-1)!]`
`hArr n-3 gt 4 hArr n gt7`