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Compute the following sum, $\sum_{k=1}^{n}\left(a_{k+1}-a_{k-1}\right)$ (Hint: write $\left.a_{k+1}-a_{k-1}=a_{k+1}-a_{k}+a_{k}-a_{k-1}\right)$

$$a_{n+1}-a_{1}+a_{n}-a_{0}$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

00:48

Show that $\sum_{k=1}^{n}\…

01:00

Show that $\sum_{k=1}^{n} …

03:05

Find the sum.$$\sum_{k…

00:29

In this question, we consider the summation under k, plus b k case from 1 to end. If we expand this submission here, we should equal to that a 1 plus 1 plus 82 plus p 2, plus to the i n, plus p n, and now we can rearrange the term to pluto in and then we drop the b into 1 plus plus to The here and this what we can write state summation, okay case to 1 to n plus, and this only in the same thing day case.

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