Question

Quality AnsWer needed=_=​

Answer 1

$\frac{1}{5 + x} = \frac{1}{5} (1 + \frac{x}{5} ) ^{ - 1} \\ = \frac{1}{5} (1 - \frac{x}{5} + (\frac{x}{5}) ^{2} - (\frac{x}{5}) ^{3} + .............) \\ = \frac{1}{5} (1 - \frac{x}{5} \: + \frac{ {x}^{2} }{25} - \frac{ x ^{3}}{125 \: } \: +..............)</p><p> \\ the \: expansion \: is \: only \: valid \: if \: | \frac{x}{5} | < 1.$

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Answer 2

Answer:

\begin{gathered} \frac{1}{5 + x} = \frac{1}{5} (1 + \frac{x}{5} ) ^{ - 1} \\ = \frac{1}{5} (1 - \frac{x}{5} + (\frac{x}{5}) ^{2} - (\frac{x}{5}) ^{3} + .............) \\ = \frac{1}{5} (1 - \frac{x}{5} \: + \frac{ {x}^{2} }{25} - \frac{ x ^{3}}{125 \: } \: +..............) < /p > < p > \\ the \: expansion \: is \: only \: valid \: if \: | \frac{x}{5} | < 1.\end{gathered}

5+x

1

=

5

1

(1+

5

x

)

−1

=

5

1

(1−

5

x

+(

5

x

)

2

−(

5

x

)

3

+.............)

=

5

1

(1−

5

x

+

25

x

2

−

125

x

3

+..............)</p><p>

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HOPE I HELPED : D