Problem

Solve each problem. Nancy Bondy's aunt has promis…

02:20

Problem 40 Hard Difficulty

Use a formula for $S_{n}$ to evaluate each series.
$$
\sum_{i=1}^{2000} i
$$

Answer

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Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 2

Arithmetic Sequences

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Video Transcript

we're being asked to find the some of this particular Siri's. So no, this were given the Siris in summation notation. So the first thing you need to figure out is how many terms you're in the sequence? Well, because we're going from I equals one till I equals 2000. That means you're trying to find the some of the 1st 2000 terms, which means that N is equal to 2000. Next, we want to find the first turn, the Siri's. To do this, we substitute one in place of I. Well, that's still just gonna leave us with one now because we're trying to find the some of the 1st 2000 terms. What's find? What is the 2000 turn in the sequence? So they do this. We was substitute 2000 place of I, which is still just going to be 2000. So because we have end ace of one, an ace of 2000, which is kind of like our ace event Valium, we're going to use the first of our two summation formulas, which, if you recall, is ESA Ben is equal to end over to times a serve one plus a seven. So now we can sues the values that we just found to find ourselves. So a substitute them it we're gonna have s of 2000 equals will end, which is 2000 divided by two times one plus 2000. All right, well, first, we're gonna have to divide 2000 by two, which is just 1000 and nimble. Add one plus 2000, which is 2001. So in order to find s of 2000, we now need to multiply. So eso 2000 will equal to well 1000 times. 2001 is equal to two million. 1000. So perfect with found the some of this series It's 2,001,000.

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Margaret L. Lial , John Hornsby

Beginning and Intermediate Algebra

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Problem

Solve each problem. Nancy Bondy's aunt has promis…

Problem 40 Hard Difficulty

Use a formula for $S_{n}$ to evaluate each series.
$$
\sum_{i=1}^{2000} i
$$

Answer

Related Courses

Beginning and Intermediate Algebra

Related Topics

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Video Transcript

Margaret L. Lial , John Hornsby

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Continuity - Overview

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Margaret L. Lial , John HornsbyBeginning and Intermediate Algebra

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Margaret L. Lial , John Hornsby

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