Write the middle term in the expansion of 2 x2-3-3-2 x210-

( 2x^2/3+3/2x^2 )^10. Here n =10, which is even number So, ( 10/2+1 )th term i.e. 6th term is the middle term. T_6 =T_5+1=^10C_5 ( 2x^2/3 )^10 5 ( 3/2x^2 )^5 ...

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Standard XII

Mathematics

Middle Terms

Write the mid...

Question

Write the middle term in the expansion of ${(\frac{2 x^{2}}{3} + \frac{3}{2 x^{2}})}^{10} .$

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Solution

${(\frac{2 x^{2}}{3} + \frac{3}{2 x^{2}})}^{10} .$

Here n =10, which is even number

So, $(\frac{10}{2} + 1) t h$ term i.e. 6th term is the middle term.

$T_{6} = T_{5 + 1} =^{10} C_{5} {(\frac{2 x^{2}}{3})}^{10 - 5} {(\frac{3}{2 x^{2}})}^{5} =^{10} C_{5} {(\frac{2 x^{2}}{3})}^{5} {(\frac{3}{2 x^{2}})}^{5} = 252$

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Write the middle term in the expansion of (2x23+32x2)10.

(2x23+32x2)10. Here n =10, which is even number So, (102+1)th term i.e. 6th term is the middle term. T6=T5+1=10C5(2x23)10−5(32x2)5=10C5(2x23)5(32x2)5=252

Write the middle term in the expansion of ${(\frac{2 x^{2}}{3} + \frac{3}{2 x^{2}})}^{10} .$