Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Calculus Volume 2

Key Equations

Calculus Volume 2Key Equations

Key Equations

Harmonic series n=11n=1+12+13+14+n=11n=1+12+13+14+
Sum of a geometric series n=1arn1=a1rfor|r|<1n=1arn1=a1rfor|r|<1
Divergence test Ifan0asn,n=1andiverges.Ifan0asn,n=1andiverges.
p-series n=11np{converges ifp>1diverges ifp1n=11np{converges ifp>1diverges ifp1
Remainder estimate from the integral test N+1f(x)dx<RN<Nf(x)dxN+1f(x)dx<RN<Nf(x)dx
Alternating series n=1(−1)n+1bn=b1b2+b3b4+orn=1(−1)n+1bn=b1b2+b3b4+or
n=1(−1)nbn=b1+b2b3+b4n=1(−1)nbn=b1+b2b3+b4
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
    Access for free at https://openstax.org/books/calculus-volume-2/pages/1-introduction
  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
    Access for free at https://openstax.org/books/calculus-volume-2/pages/1-introduction
Citation information

© Feb 5, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.