Question

Find infinite sum from 1 to infinity of 1/1 n²
A) 2/1
B) 4/π
C) π² /6
D) π/6

Answer 1

To find the infinite sum from 1 to infinity of 1/(n^2), we can use the formula for the sum of an infinite geometric series. The sum approaches 1 as n goes to infinity.

Step-by-step explanation:

To find the infinite sum from 1 to infinity of 1/(n^2), we can use the formula for the sum of an infinite geometric series. The formula is S = a/(1 - r), where S is the sum, a is the first term, and r is the common ratio. In this case, a = 1 and r = 1/n^2. Therefore, we have S = 1/(1 - 1/n^2) = n^2/(n^2 - 1).

To simplify this fraction, we can use the difference of squares identity: n^2 - 1 = (n - 1)(n + 1). So the sum becomes S = (n^2)/((n - 1)(n + 1)).

As n approaches infinity, the terms (n - 1) and (n + 1) become very similar, so we can approximate their product as n^2. Therefore, the sum approaches n^2/n^2 = 1 as n goes to infinity.