MathDB

Today's calculation of Integral 30

Source: 1990 Shibaura Institute of Technology

May 31, 2005

calculusintegrationalgebrapartial fractionscalculus computations

Problem Statement

A sequence

\{a_n\}

is defined by

a_n=\int_0^1 x^3(1-x)^n dx\ (n=1,2,3.\cdots)

Find the constant number

c

such that

\sum_{n=1}^{\infty} (n+c)(a_n-a_{n+1})=\frac{1}{3}