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

Let T_r+1 #160;be the term independent of x #160;in the given expansion. ∴ T_r+1=^4C_rx^4 r(1/x)^r=^4C_rx^4 r/x^r=^4C_rx^4 2r For the term indepen ...

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Byju's Answer

Standard XI

Mathematics

Term Independent of X

Find the term...

Question

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

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Solution

Let $T_{r + 1}$ be the term independent of x in the given expansion.
$∴ T_{r + 1} =^{4} C_{r} x^{4 - r} {(\frac{1}{x})}^{r} =^{4} C_{r} \frac{x^{4 - r}}{x^{r}} =^{4} C_{r} x^{4 - 2 r}$
For the term independent of x the power of x ,should be zero.
$∴ 4 - 2 r = 0 ⟹ r = 2$
$⟹ T_{2 + 1} = T_{3}$ , is the independent term of the expansion.

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

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

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