Question

write down the general term in the binomial expansion of (X+A)n.​

Answer 1

$\underline{\textsf{To find:}}$

$\textsf{General term in the binomial exansion of}\;\mathsf{(x+a)^n}$

$\underline{\textsf{Solution:}}$

$\underline\mathsf{BINOMIAL THEOREM:}$

$\mathsf{For\;any\;natural\;number\;n,}$

$\mathsf{(x+a)^n=^nC_0\,x^n\,a^0\;+\;^nC_1\,x^{n-1}\,a^1\;+\;^nC_2\,x^{n-2}\,a^2\;+........+\;^nC_{n-1}\,x^1\,a^{n-1}\;+\;^nC_n\,x^0\,a^n}$

$\mathsf{The\;expansion\;of\;(x+a)^n\;contains\;n+1\;terms}$

$\textsf{This can be written as}$

$\mathsf{(x+a)^n=\displaystyle\sum^{r=n}_{r=0}\;\;^nC_r\,x^{n-r}\,a^r}$

$\therefore\textsf{The general term is}$

$\boxed{\mathsf{T_{r+1}=^nC_r\,x^{n-r}\,a^r}}$

$\underline{\textsf{Find more:}}$

Prove that there is no term involving x^5 int he expansion of (2x^2-3/x)^11

https://brainly.in/question/792606

Answer 2

Answer:

It is known that  the general term (T)  

r+1

​  

 {which is the  (r+1) in the

binomial expansion of (a+b)  

n

 is given by T  

r+1

​  

=  

n

C  

r

​  

a  

n−r

b  

r

 

Thus, the general term in the expansion of (x  

2

−y)  

6

 is

T  

r+1

​  

=  

6

C  

r

​  

(x  

2

)  

6−r

(−y)  

r

=(−1)  

r

6C  

r

​  

x  

12−2r

y  

r

Step-by-step explanation: