Question

prove that n!/(n-r)!r!+n!/(n-r+1)!(r-1)!=(n+1)!/r!(n-r+1)!

Answer 1

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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

Thanks..

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Answer 2

Step-by-step explanation:

hope you will get it to be useful