Find each sum. 2+4+6+⋯+2 n

Name: Problem 40, Chapter 11: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-05-09T20:07:46-08:00
Duration: 57 s
Channel: Julie Silva
Description: Find each sum. 2+4+6+⋯+2 n

step 1 We're being asked to find the sum of the series 2 plus 4 plus 6 all the way up till plus 2N. So

Question

Find each sum. $$ 2+4+6+\cdots+2 n $$

   Find each sum.
$$
2+4+6+\cdots+2 n
$$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 11, Problem 40

Instant Answer

Solved by Expert Julie Silva

05/09/2020

Step 1

The given sequence is $2, 4, 6, \ldots, 2n$. This is an arithmetic sequence where each term increases by 2. Show more…

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Find each sum. $$ 2+4+6+\cdots+2 n $$

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Key Concepts

Arithmetic Sequence

An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant. This property allows for the prediction of any term in the sequence based on its position, and it forms the basis for deriving formulas for various characteristics of the sequence.

Arithmetic Series Sum Formula

The arithmetic series sum formula, often given as S = (n/2)(a? + a?), is used to compute the sum of all terms in an arithmetic sequence. This formula works by pairing terms from the start and end of the sequence, thus providing a quick and effective method for summing a sequence with a constant difference.

Factorization in Summation

Factorization refers to the process of extracting a common factor from each term in an expression or sequence. In the context of sequences, recognizing a common factor can simplify the sum by transforming it into a multiple of a simpler series, making calculations more straightforward.

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