1-Find-the-term-independent-of-x-in-the-expansion-of-x-2-x-10-

Question Number 27809 by das47955@mail.com last updated on 15/Jan/18

(1) Find the term independent

of x in the expansion of

{(x - \frac{2}{x})}^{10}

Answered by 8/mln(naing)060691 last updated on 15/Jan/18

{(r + 1)}^{th} term =^{10} C_{r} x^{10 - r} {(- \frac{2}{x})}^{r}

=^{10} C_{r} . x^{10 - r} {(- 2)}^{r} x^{- r}

=^{10} C_{r} {(- 2)}^{r} x^{10 - 2 r}

To get the term independent of x,

put 10 - 2 r = 0 \Rightarrow r = 5

∴ the term independent of x =^{10} C_{5} {(- 2)}^{5}

Commented by das47955@mail.com last updated on 15/Jan/18

wow . i need this process

Commented by das47955@mail.com last updated on 15/Jan/18

really thanks \dots . .

Answered by mrW2 last updated on 15/Jan/18

{(x - \frac{2}{x})}^{10} = \underset{k = 0}{\sum^{10}} C_{k}^{10} x^{k} {(- \frac{2}{x})}^{10 - k}

= \underset{k = 0}{\sum^{10}} C_{k}^{10} {(- 2)}^{10 - k} x^{2 k - 10}

2 k - 10 = 0

k = 5

x - i n d e p e n d e n t t e r m i s

C_{5}^{10} {(- 2)}^{5} = - 8064

Commented by das47955@mail.com last updated on 15/Jan/18

T hanks \dots .