Mathematics

You need to find the $x^6$ coefficient in a product of two functions, each with a known series. Start by writing out the Maclaurin series for $(1+x)^3$ and $\ln(1+x)$ separately, then multiply them together—collecting all the ways that terms can combine to give $x^6$. This is a convolution problem: you're looking for every pair of terms whose powers add to 6.

You need to find the $x^6$ coefficient in a product of two functions, each with a known series. Start by writing out the Maclaurin series for $(1+x)^3$ and $\ln(1+x)$ separately, then multiply them together—collecting all the ways that terms can combine to give $x^6$. This is a convolution problem: you're looking for every pair of terms whose powers add to 6.