In the coefficients of rth, `(r+1)t h ,a n d(r+2)t h` terms in the binomial expansion of `(1+y)^m` are in A.P., then prove that `m^2-m(4r+1)+4r^2-2=0.`

Explanation

To prove that the coefficients of the \( r \)-th, \( (r+1) \)-th, and \( (r+2) \)-th terms in the binomial expansion of \( (1+y)^m \) are in Arithmetic Progression (A.P.), we start with the coefficients of these terms.

### Step 1: Identify the coefficients
The coefficients of the \( r \)-th, \( (r+1) \)-th, and \( (r+2) \)-th terms in the expansion of \( (1+y)^m \) are given by:
- Coefficient of \( r \)-th term: \( \binom{m}{r} \)
- Coefficient of \( (r+1) \)-th term: \( \binom{m}{r+1} \)
- Coefficient of \( (r+2) \)-th term: \( \binom{m}{r+2} \)

...