Question

If Pn denotes the product of all the co-efficients in the expansion of (1+x)^n

, then pn+1/pn

is equal​

Answer 1

Answer:

Step-by-step explanation:

(1+x)  

n

 

P  

n+1

​  

=  

n+1

​  

C  

0

​  

×  

n+1

​  

C  

1

​  

×  

n+1

​  

C  

2

​  

×........×  

n+1

​  

C  

n+1

​  

 

P  

n

​  

=  

n

​  

C  

0

​  

×  

n

​  

C  

1

​  

×  

n

​  

C  

2

​  

×........×  

n

​  

C  

n

​  

 

∏  

r=0

n

​  

 

n

​  

C  

r

​  

 

n+1

​  

C  

r

​  

 

​  

(∵  

n+1

​  

C  

n+1

​  

=1)

=∏  

r=0

n

​  

 

r!(n+1−r)!

(n+1)!

​  

×  

n!

r!(n−r)!

​  

 

=∏  

r=0

n

​  

 

(n−r+1)

(n+1)

​  

 

=(n+1)  

n

∏  

r=0

n

​  

 

n−r+1

1

​  

 

=  

(n+1)!

(n+1)  

n

 

​