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  • Find the term independent of x, where x≠0, in the expansion of (3x^2/2-1/3x)^15

Find the term independent of x, where x≠0, in the expansion of  \left ( \frac{3x^{2}}{2} - \frac{1}{3x} \right )^{15}

Answers (1)

\left ( \frac{3x^{2}}{2} - \frac{1}{3x} \right )^{15}............... (Given)

T_{r+1}=^{15}\textrm{C}_{r}\left ( \frac{3x^{2}}{2} \right )^{15-r}\left ( -\frac{1}{3x} \right )^{r}      ……. (from standard formula of Tr+1)

T_{r+1}=^{15}\textrm{C}_{r}\left ( -1 \right )^{r}3^{15-2r}2^{r-15}X^{30-3r}  …… (i)

Now, for x,

30 – 3r = 0

→ r = 10

Substituting the value of r in eq (i),

T_{r+1}=^{15}\textrm{C}_{10}3^{-5}2^{-5}

            =^{15}\textrm{C}_{10}\left ( \frac{1}{6} \right )^{5}

Posted by

infoexpert22

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