C0900TextPages_page_31

C0900TextPages | page 31 | https://thedailydialectics.com/pdfs/education/C0900TextPages/C0900TextPages.pdf

75. Euler’s Constant Let | 1 1 S,= Nosltstee te. a 2 n (a) Show that In(n + 1) < S, < 1+ Inn. (b) Show that the sequence {a,,} = {5,, — Inn} is bounded. (c) Show that the sequence {a,,} is decreasing. (d) Show that a,, converges to a limit y (called Euler’s con- SECTION 9.3 The Integral Test and…