The series in question is the sum of the terms of the sequence given by 1/n^2, where n ranges from 1 to infinity. In other words, we need to find the value of:

1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ...

To find the sum of this infinite series, we can use a mathematical concept called the convergence of a series.

Convergence of the Series:
The series 1/n^2 is a special type of series known as a p-series. A p-series is defined as a series of the form 1/n^p, where p is a positive constant. The convergence of a p-series depends on the value of p.

In our case, p = 2, which means we have a p-series with p = 2. It is known that a p-series with p > 1 converges, which implies that our series converges.

Calculating the Sum:
To find the sum of the series, we can use a mathematical formula derived specifically for p-series. The formula for the sum of a p-series is given by:

Sum = 1/1^p + 1/2^p + 1/3^p + 1/4^p + ... = (1/1^(p-1))/((p-1)) + (1/2^(p-1))/((p-1)) + (1/3^(p-1))/((p-1)) + (1/4^(p-1))/((p-1)) + ...

In our case, p = 2, so we can substitute the value of p into the formula:

Sum = (1/1^(2-1))/((2-1)) + (1/2^(2-1))/((2-1)) + (1/3^(2-1))/((2-1)) + (1/4^(2-1))/((2-1)) + ...
= 1/1 + 1/2 + 1/3 + 1/4 + ...

The sum of our series is equal to the sum of the harmonic series, which is known to diverge. In other words, the sum of our series is infinite.

Conclusion:
The sum of the series 1/n^2, where n ranges from 1 to infinity, is infinite. This is because the series is a p-series with p = 2, and the sum of a p-series with p > 1 is infinite.