the coifficent of {r-1}th ,r th ,{r-1}th term in expansion of {x+1}n are in the ratio 1:3:5,find n&r.

The problem provides the equations that relates the
binomial coefficients of the and terms, such
that:

3(C_n^r)

Using the factorial formulas
yields:

Since and
yields:

3/5

1)!)

You need to solve for n and r the system of simultaneous
equations, such that:

3(n-r-1)):}

=> {(-8r + 2n = 6),(8r - 3n = -13):} => -n = -7 => n = 7 r =
(n-3)/4 => r = (7-3)/4 => r =
1

Hence, evaluating r and n, under the given
conditions, yields and .