The-sum-of-integers-from-1-to-100-that-are-divisible-by-2-or-5-is-

Question Number 43765 by peter frank last updated on 15/Sep/18

The sum of integers from 1 to 100 that

are divisible by 2 or 5 is_____.

Answered by math1967 last updated on 15/Sep/18

s u m o f d i v i s i b l e b y 2 = S_{2}

s u m o f d i v i s i b l e b y 5 = S_{5}

s u m o f d i v i s i b l e b y b o t h 2 a n d 5 = S_{10}

∴ n (S_{2} \cup S_{5}) = n (S_{2}) + n (S_{5}) - n (S_{2} \cap S_{5})

= {2 + 4 + \dots 100} + {5 + 10 + . . 100}

- {10 + 20 + \dots 100}

= \frac{50}{2} (2 \times 2 + 49 \times 2) + \frac{20}{2} (2 \times 5 + 19 \times 5)

- \frac{10}{2} (2 \times 10 + 9 \times 10)

[u s i n g S_{n} = \frac{n}{2} {2 a + (n - 1) \times d}]

= 2550 + 1050 - 550 = 3050 A n s

Facebook Tweet Pin