The sum of reciprocal squares of natural numbers is analyzed by direct geometric principle

2022-05-08 0 By

We all know that the sum of the reciprocal of the squares of the natural numbers is equal to PI ^2/6, which was proved by Euler and made famous by him.There are a lot of proofs about this series, but Euler’s method is still the most classical and easy to understand, and you can refer to the relevant materials. It contains mathematical thinking worth learning. In this paper, we have obtained the properties of the series from the point of view of geometry except for the first term 1, namely 1/2^2+1/3^2+1/4^2+…How is the sum of phi distributed as follows if I have a square of one x1, and if I divide it into four halves I get one half squared, and the other one is one third squared then I get that the sum of the reciprocal squares of all the natural numbers except one is less than one, and it turns out to be true.Therefore, the ingenious geometric principle visually expresses the abstract series principle, and the method is easy to understand and worth our reference and learning.