Today's calculation of Integral 465
Source: 2009 University of Electro-communication entrance exam
June 28, 2009
calculusintegrationcalculus computations
Problem Statement
Compute \int_0^1 x^{2n\plus{}1}e^{\minus{}x^2}dx\ (n\equal{}1,\ 2,\ \cdots) , then use this result, prove that \sum_{n\equal{}0}^{\infty} \frac{1}{n!}\equal{}e.