Question

 Expansion of log(1+x)1/x in ascending powers of x is​

Answer 1

I can't do this sum ...so sorry yrr

Thank you ...

Brinlists Answer

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Answer 2

Answer:

Expansion of $log(1+x)1/x$ is $x-x^{2} /2+x^{3}/3$....

Step-by-step explanation:

Given:

$log(1+x)1/x$

To Find:

x-x^{2} /2+x^{3}/3

Solution:

Assume $f(x)=log(1+x)1/x$

Now, the expansion becomes,

$f(x)=f(0)+xf'(0)+(x^{2} /2!)f"(0)$

when x=0 then,

$f(0)=log(1+0)1/0$

Similarly,

$f'(x)=1/x(1+x)$

Hence, the expansion of log(1+x)1/x is x-x^{2} /2+x^{3}/3