Question

How do you find the fourth term of `(x+1/3)^7`?

Answer 1

`4` th term is `35/27*x^4`

Explanation:

Binomial theorem:
`(a + b)^n =(nC_0) a^nb^0+ (nC_1) a^(n-1)b^1 +(nC_2) a^(n-2)b^2 +...... (nC_n)b^n`

Here `(a=x ; b=1/3 , n= 7)`

We know `nC_r= (n!)/(r!(n-r)!) :. 7C_3=35`

`4`th term is `(7C_3)x^(7-3)*(1/3)^3 = 35*x^4*1/27 =35/27*x^4` [Ans]