How-to 7 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

Sum[1 / n ^ 2, {n, 1, Infinity}]

Output

Pi^2/6

Step 2

Sum[1 / n ^ 2, {n, 1, 100}]

Output

1589508694133037873112297928517553859702383498543709859889432834803818131090369901/972186144434381030589657976672623144161975583995746241782720354705517986165248000

Step 3

Sum[1. / n ^ 2, {n, 1, 100}]

Output

1.6349839001848923

Step 4

Limit[Abs[Pi ^ 2 / 6 - Sum[1 / n ^ 2, {n, 1, k}]], k -> Infinity]

Output

Step 5

Sum[1 / n ^ s, {n, 1, Infinity}]

Output

Zeta[s]

Step 6

Pi z Product[1 - z ^ 2 / n ^ 2, {n, 1, Infinity}]

Output

Pi*z*Product[1 - z^2/n^2, {n, 1, Infinity}]

Step 7

Product[1 / (1 - Prime[k] ^ -s), {k, 1, Infinity}]

Output

Product[(1 - Prime[k]^(-s))^(-1), {k, 1, Infinity}]

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Evaluate infinite sums and products

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