Math Homework Series Problem

Problem Representative OA math/series task: students are assigned a sequence of math problems defined by a rule; compute the required aggregate — e.g. given the rule "problem i has value f(i)", count or sum the values in [1, n] satisfying a condition (divisibility, digit property, or a recurrence).

Input / Output

• Input: the sequence parameters (e.g. n, the rule constants).
• Output: the count/sum requested, often modulo 1e9+7.

Constraints

• n can be up to 10^9 in such problems — a closed-form or O(log n)/O(√n) derivation is expected, not brute-force iteration.

Example

• e.g. "sum of all numbers ≤ n divisible by 3 or 5": use arithmetic-series sums S(k) = k*(k+1)/2 with inclusion–exclusion: 3S(n/3) + 5S(n/5) − 15*S(n/15).

Expected approach

• Translate the story into the underlying sequence, then reach for: arithmetic/geometric series formulas, inclusion–exclusion, digit DP for digit-property counts, or matrix power for linear recurrences. Watch overflow (use 64-bit / modular arithmetic) and off-by-one at range boundaries.