Question

afè If In = Sx Va-xaha fay for: then prove that:
(2n + 3) In = 2an In-1-2x" (a - x)1/2​

Answer 1

Answer:

n + 1/n

Step-by-step explanation:

We have to prove the ratio of sum of odd terms to sum of even terms of an arithmetic series to be  

n

n+1

​

.

Since there are 2n+1 terms there will be n+1 terms.

Let us consider the odd terms and even terms to be two different series.

These series will have common difference 2d, where d is the common difference of original series.

Let a be the first term.

Sum of odd term series =  

2

n+1

​

(2a+n×2d)     ....(i)

Sum of even term series =  

2

n

​

(2(a+d)+(n−1)×2d)=d  

2

n

​

(2a+n×2d)     ....(ii)

The ratio  

2

n

​

(2a+n×2d)

2

n+1

​

(2a+n×2d)

​

=  

n

n+1

​