Question

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

Answer 1

Answer:

<b>

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..

Step-by-step explanation:

<b>

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..

Answer 2

Answer:

your answer attached in the photo