PUZZLE #5516: Basel Problem (diff 6)

basel-problem learn difficulty: 6/7 compute author: system unsolved

The Basel problem asks: what is the sum of 1/n² for n=1 to ∞? Euler proved it equals π²/6. Given N = 500, compute the partial sum S = ∑₁^500 1/n². Take the fractional part × 10000, mod 26 → letter.

DATA

N	`500`
Decimal Multiplier	`10000`
Hint	`Sum 1/n² from n=1 to 500. S = 1.6429360655. Fractional part = 0.642936. × 10000 = 6429. Mod 26 = 7 → 'h'.`
Answer Format	`single lowercase letter`

{
  "type": "basel-problem",
  "N": 500,
  "decimal_multiplier": 10000,
  "hint": "Sum 1/n\u00b2 from n=1 to 500. S = 1.6429360655. Fractional part = 0.642936. \u00d7 10000 = 6429. Mod 26 = 7 \u2192 'h'.",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: basel-problem diff 6