Someone can help me ?
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Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:
for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:
This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
Since 5 is divisible by 10 and 5, we can factor out a 5 from both terms.