Integral test

Unit 11.3 of Math 152

Integral for convergence

• In order for this to work

  • $a_n=f(n)$

    • The function must be

      • positive
      • continuous
      • decreasing
      • $x\ge 1$

• Basic idea

  • Lets say we have a series ${\sum }_{n=1}^{\infty }{a}_n$ we could in order to find out if the series is convergent turn it into an improper integral
    • ${\int }_1^{\infty }{a}_{n}dx$

      • and if this integral gives us a constant the series converges