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Chapter 19: Problem 4

Find the sum of the first 40 positive integers.

Short Answer

Expert verified
Answer: The sum of the first 40 positive integers is 820.

Step by step solution

01

Identify the formula

We will use the sum of arithmetic series formula, which is S = (n * (n + 1))/2. In this case, n=40 as it's the sum of the first 40 positive integers.
02

Substitute the values in the formula

Now, substitute the value of n=40 in the formula S = (n * (n + 1))/2. S = (40 * (40 + 1))/2
03

Simplify the expression

Now, simplify the expression to find the sum. S = (40 * (41))/2
04

Perform the calculations

Perform the calculations to find the sum. S = (40 * 41) / 2 S = 1640 / 2
05

Find the sum

Finally, find the sum S = 820. Hence, the sum of the first 40 positive integers is 820.

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Most popular questions from this chapter

Find the sum of the squares of the first 20 positive integers.

Obtain the Maclaurin series expansion for \(f(x)=\cosh x\).

Find the sum of the infinite geometric series with first term 2 and common ratio \(\frac{1}{2}\).

Find the sum of the first five terms of the arithmetic sequence with first term 3 and common difference 5 .

A geometric series has \(S_{3}=\frac{37}{8}\) and \(S_{6}=\frac{3367}{512}\). Find the first term and the common ratio.
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