The remainder, when 1 + (1 × 2) + (1 × 2 × 3) + ... + (1 × 2 × 3 × ... × 500) is divided by 8, is

examrobotsa's picture

Submitted by examrobotsa on

Q: 61 (CAPF/2024)
The remainder, when 1 + (1 × 2) + (1 × 2 × 3) + ... + (1 × 2 × 3 × ... × 500) is divided by 8, is

question_subject: 

Mathematics

question_exam: 

CAPF

The series described is the sum of factorials. Due to properties of factorials and division by 8, every term from 4! onwards is divisible by 8, leaving only the first few terms to determine the remainder. Calculating gives a remainder of 3.