MathDB
Today's calculation of Integral 129

Source: Osaka Institute of Tecnology entrance exam 2006

July 26, 2006
calculusintegrationtrigonometrylimitcalculus computations

Problem Statement

The sequence {an}\{a_{n}\} is defined as follows. a1=π4, an=∫012(cos⁡πx+an−1)cos⁡πx dx  (n=2,3,⋯ )a_{1}=\frac{\pi}{4},\ a_{n}=\int_{0}^{\frac{1}{2}}(\cos \pi x+a_{n-1})\cos \pi x\ dx\ \ (n=2,3,\cdots) Find lim⁡n→∞an\lim_{n\to\infty}a_{n}.
Back to ProblemsView on AoPS