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Evaluate the given sum.$$\sum_{k=1}^{5}\left(2 k^{2}-1\right)$$

$$105$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 5

Sigma Notation and Areas

Integrals

Oregon State University

Harvey Mudd College

Idaho State University

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.

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Okay. Hello. So here we have to some we have K. Going from 3 to 5 of negative one to the K over K factorial. So that's just negative one over. We started three so negative 1/3 factorial and then plus 1/4 factorial and then minus 1/5 factorial. That's going to be just negative 1/6. And then we get plus one 24th and then we have a minus 1/1 20. So we get a common denominator here of 1 20. Then we get negative 20 plus five minus one, all divided by 225 which gives us negative 16 over 120 Which then reduces to negative 2/15.

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