PUZZLE #5585: Basel Problem (diff 7)

basel-problem learn difficulty: 7/7 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 = 1000, compute the partial sum S = ∑₁^1000 1/n². Take the fractional part × 10000, mod 26 → letter.

DATA

N	`1000`
Decimal Multiplier	`10000`
Hint	`Sum 1/n² from n=1 to 1000. S = 1.6439345667. Fractional part = 0.643935. × 10000 = 6439. Mod 26 = 17 → 'r'.`
Answer Format	`single lowercase letter`

{
  "type": "basel-problem",
  "N": 1000,
  "decimal_multiplier": 10000,
  "hint": "Sum 1/n\u00b2 from n=1 to 1000. S = 1.6439345667. Fractional part = 0.643935. \u00d7 10000 = 6439. Mod 26 = 17 \u2192 'r'.",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: basel-problem diff 7