General Term
Category : JEE Main & Advanced
The general term of the expansion is \[{{(r+1)}^{th}}\] term usually denoted by \[{{T}_{r+1}}\] and \[{{T}_{r+1}}{{=}^{n}}{{C}_{r}}{{x}^{n-r}}{{y}^{r}}\]
- In the binomial expansion of \[{{(x-y)}^{n}},\,{{T}_{r+1}}={{(-1)}^{r}}{{\,}^{n}}{{C}_{r}}{{x}^{n-r}}{{y}^{r}}\]
- In the binomial expansion of \[{{(1+x)}^{n}},\,{{T}_{r+1}}{{=}^{n}}{{C}_{r}}{{x}^{r}}\]
- In the binomial expansion of \[{{(1-x)}^{n}},\,{{T}_{r+1}}={{(-1)}^{r}}{{\,}^{n}}{{C}_{r}}{{x}^{r}}\]
- In the binomial expansion of \[{{(x+y)}^{n}}\], the pth term from the end is \[{{(n-p+2)}^{th}}\] term from beginning.