Try to prove this equation (HARD)
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Be tough.... harder than it
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To prove
n! / r!(n-r)! + n! / (r-1)! (n-r+1)! = (n+1)! / r!(n-r+1)!
L.H.S
n! / (r)(r-1)! (n-r)! +n! / (r-1)! (n-r+1)(n-r)!
n! / (r-1)! (n-r)! will be common
so,
n! / (r-1)! (n-r)! *[ 1/r + 1/(n-r+1) ]
n! / (r-1)! (n-r)! *[ n-r+1+r / nr-r2 +r ]
we will get ,
n! / (r-1)! (n-r)! / * [n+1 / r(n-r+1)]
(n!) (n+1) / (r-1)! (r) (n-r)! (n-r+1)
(n+1)! / r! ( n-r+1)!
L.H.S=R.H.S
Hope u got it!
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