+738 What is the coefficient of \(x^3\) in this expression?
\((x^4 + x^3 + x^2 + x + 1)^4\)
thank you to whoever helps :)
+37146 According to WolframAlpha it is 20
https://www.wolframalpha.com/input/?i=%28x%5E4+%2Bx%5E3+%2Bx%5E2%2Bx%2B1%29%5E4
+23252 The coefficients of the final (multiplied-out) terms form tetrahedral numbers: 1, 4, 10, 20, 34, 56, ...
So, the coefficient of the constant term (the 1) and the x16-term are both 1.
The coefficient of the x-term and the x15-term are both 4.
The coefficient of the x2-term and the x14-term are both 10.
The coefficient of the x3-term and the x13-term are boh 20
Etc.
To find the nth-term of the tetrahedral numbers, you can use this formula: n · (n + 1)·(n + 2) / 6
