Find the 7th term in the expansion of

Question:

Find the 7 th term in the expansion of $\left(3 x^{2}-\frac{1}{x^{3}}\right)^{10}$.

Solution:

We need to find the 7th term of the given expression.

Let it be T7

Now, we have

$T_{7}=T_{6+1}$

$={ }^{10} C_{6}\left(3 x^{2}\right)^{10-6}\left(\frac{-1}{x^{3}}\right)^{6}$

$={ }^{10} C_{6}\left(3^{4}\right)\left(x^{8}\right)\left(\frac{1}{x^{18}}\right)$

 

$=\frac{10 \times 9 \times 8 \times 7 \times 81}{4 \times 3 \times 2 \times x^{10}}=\frac{17010}{x^{10}}$

Thus, the 7 th term of the given expression is $\frac{17010}{x^{10}}$

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