Explanation
Coefficient of xr and xr+1 are equal.
Coefficient of Tr+1= Coefficient of Tr+2
⇒55Cr(2)55−r(13)r=55Cr+1(2)54−r(13)r+1
. 55!(55−r)!r!(2)=55!(54−r)!(r+1)!13
⇒6(r+1)=55−r
⇒r=7
So, the terms will be 8th and 9th
Consider given the expression,
{{\left( x+y \right)}^{50}}+{{\left( x-y \right)}^{50}}
We know that,
{{\left( x+y \right)}^{n}}={}^{n}{{C}_{0}}{{x}^{n}}{{+}^{n}}{{C}_{1}}{{x}^{n-1}}y{{+}^{n}}{{C}_{2}}{{x}^{n-2}}{{y}^{2}}+{{......}^{n}}{{C}_{r}}{{x}^{n-r}}{{y}^{r}}{{.....}^{n}}{{C}_{n}}{{y}^{n}}
Now,
{{\left( x+y \right)}^{50}}+{{\left( x-y \right)}^{50}}=2{{[}^{50}}{{C}_{0}}{{x}^{50}}{{+}^{50}}{{C}_{2}}{{x}^{50-2}}y{{+}^{50}}{{C}_{4}}{{x}^{50-4}}{{y}^{4}}+{{......}^{50}}{{C}_{r}}{{x}^{50-r}}{{y}^{r}}{{.....}^{50}}{{C}_{50}}{{y}^{50}}
Hence, there are 26 terms
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