Prove that the coefficient of the middle term in the expansion of `(1+x)^(2n)` is equal to the sum of the coefficients of middle terms in the expansion of `(1+x)^(2n-1)`

Explanation

Since `2 {n}` is even middle term `=(frac{2 n}{2}+1)^{ {th }}=(n+1)^{ {th }}` term `=T_{n+1}`


we know that general term of expansion `(a+b)^{n}` is -


`{T}_{{n}+1}=\ ^{{n}} {C}_{{r}} {a}^{{n}-{r}} {b}^{{r}}`


here, `r=n, n=2 n, a=1, b=x`


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