Write the middle term in the expansion of x -1- x 10-

( x+1/x )^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 (x)^10 5 ( 1/x )^5 =^10C_5 ...

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Standard XII

Mathematics

Middle Terms

Write the mid...

Question

Write the middle term in the expansion of ${(x + \frac{1}{x})}^{10} .$

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Solution

${(x + \frac{1}{x})}^{10}$

Here n =10, which is even number.

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

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

$=^{10} C_{5}$

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Write the middle term in the expansion of (x+1x)10.

(x+1x)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(x)10−5(1x)5 =10C5

Write the middle term in the expansion of ${(x + \frac{1}{x})}^{10} .$

${(x + \frac{1}{x})}^{10}$

Here n =10, which is even number.

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

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

$=^{10} C_{5}$