ns am reading an instance in i beg your pardon the author is recognize the power series representation that \$ln(1+x)\$. Here is the parts related to the question: I think that ns get whatever except for one thing: Why execute we require to discover a specific continuous \$C\$ and not simply leave at as an arbitrarily constant? and why carry out we discover the specific continuous we need by setup x=0 and also solve the given equation?  \$egingroup\$ The logarithm is a function, meaning that it has actually a well characterized value for a given \$x\$. You can't leave an undetermined consistent in the meaning ! \$endgroup\$
Because the is not true that we have\$\$log(1+x)=x-fracx^22+fracx^33-fracx^44+cdots+C\$\$for one arbitrary consistent \$C\$. Since, when \$x=0\$, the LHS is \$0\$ and RHS is \$C\$, \$C=0\$.

You are watching: Power series representation of ln(1+x) Since the original function is \$log (1+x)\$ and also for \$x=0\$ we have actually \$log (1+0)=0\$ we need that also the collection is zero because that \$x=0\$. Thanks because that contributing response to inter-base.net Stack Exchange!

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