Find the term independent of x in 1-1x4-

Let T_r+1 be the term independent of x in the given expansion.Therefore, T_r+1=4_C_r x^4 r (1x)^r = 4_C_rx^4 rx^r=4_C_rx^4 2r For the term independent ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Binomial Expression

Find the term...

Question

Find the term independent of x in $(1 + \frac{1}{x})^{4}$ .

Open in App

Solution

Let $T_{r + 1}$ be the term independent of x in the given expansion.
Therefore,
$T_{r + 1} = {4_{C}}_{r} x^{4 - r} (\frac{1}{x})^{r} = {4_{C}}_{r} \frac{x^{4 - r}}{x^{r}} = {4_{C}}_{r} x^{4 - 2 r}$

For the term independent of x the power of x shoul be zero.
Therefore,
$4 - 2 r = 0 ⟹ r = 2$ .
Therefore,
$T_{2 + 1} = T_{3}$ term, is the term independent of x in the given expansion.

Suggest Corrections

Find the term independent of x in (1+1x)4.

Let Tr+1 be the term independent of x in the given expansion.Therefore,Tr+1=4Crx4−r(1x)r=4Crx4−rxr=4Crx4−2rFor the term independent of x the power of x shoul be zero.Therefore,4−2r=0⟹r=2.Therefore,T2+1=T3 term, is the term independent of x in the given expansion.

Find the term independent of x in $(1 + \frac{1}{x})^{4}$ .