Find the 7 th term in the expansion of 3 - 2-1 - 310 -

We need to find the 7th term of the given expression. Let it be T7 Now, we have T7=T6+1 nbsp; nbsp; nbsp; =C610(3x2)10 6 1x36=C61034x81x18=10 #215;9 ...

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Standard XII

Mathematics

General Term of Binomial Expansion

Find the 7 th...

Question

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

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Solution

We need to find the 7th term of the given expression.
Let it be T₇
Now, we have
$T_{7} = T_{6 + 1}$
$= {}^{10}C_{6} (3 x^{2})^{10 - 6} {(\frac{- 1}{x^{3}})}^{6} = {}^{10}C_{6} (3^{4}) (x^{8}) (\frac{1}{x^{18}}) = \frac{10 \times 9 \times 8 \times 7 \times 81}{4 \times 3 \times 2 \times x^{10}} = \frac{17010}{x^{10}}$

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

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Find the 7th term in the expansion of 3x2-1x310.

We need to find the 7th term of the given expression. Let it be T7 Now, we have T7=T6+1 =C610(3x2)10-6-1x36=C61034x81x18=10×9×8×7×814×3×2×x10=17010x10 Thus, the 7th term of the given expression is 17010x10

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