2. Notes
  3. JEE Main & Advanced
  4. Mathematics
  5. Binomial Theorem and Mathematical Induction
  6. General Term

JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction General Term

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.

 

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Independent Term or Constant Term keyboard_arrow_right

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