Sequence {1,1 / 4,1 / 9 , 1 / N ^ 2}, how to sum

Sequence {1,1 / 4,1 / 9 , 1 / N ^ 2}, how to sum

There are a lot of methods, but I can't answer 100 words
The most common method is to use the power series of higher numbers
Find x + (1 / 4) x ^ 2 +... + (1 / N ^ 2) x ^ n +... = s (x)
Derivation: s' (x) = ∑ (1 / N) x ^ (n-1), that is, XS' (x) = ∑ (1 / N) x ^ n
Further derivation: (XS' (x)) '= ∑ x ^ n = 1 / (1-x)
Then integral s (x) and let x = 1

Elden Ring Premiere

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