Question

Leonhard Euler was able to calculate the exact sum of the p-series with p - 2: ²s₂d −o`n−11 n ² −? 26. Use this fact to find the sum of each series.

(a) True
(b) False

Answer 1

Leonhard Euler was able to calculate the exact sum of the p-series with p - 2, and the statement (a) True is correct.

Step-by-step explanation:

The given question is asking whether it is true or false that Leonhard Euler was able to calculate the exact sum of the p-series with p - 2. To solve this, we need to understand what a p-series is and Euler's formula for its sum.

A p-series is a series of the form 1/n^p, where n starts from 1 and goes to infinity. Euler's formula for the sum of a p-series with p > 1 is given by S = 1/1^p + 1/2^p + 1/3^p + ... = pi^2/6.

However, the given question states that the p-series has p - 2, which means p = 2. In this case, the sum of the series is S = 1/1^2 + 1/2^2 + 1/3^2 + ... = pi^2/6.

Therefore, Euler was able to calculate the exact sum of the p-series with p - 2, and the statement (a) True is correct.