Question

Find the sum of all natural numbers among the first 1000 numbers which are neither divisible by 2 9 by 5

Answer 1

Answer:

99496

Step-by-step explanation:

1000 = 2 + 2n -2 , n = 1000/2 = 500

S2 = 500/2(1002) = 250500 →  sum of all natural numbers which are  divisible by 2

999 = 9 + 9n -9 , n = 999/9 = 111

S9 = 111/2(1008) = 55944 →  sum of all natural numbers which are  divisible by 9

1000 =5 + 5n -5 , n = 1000/5 = 200

S5 = 200/2(1005) = 100500 →  sum of all natural numbers which are  

divisible by 5

990 =90 +90n -90 , n = 990/90 = 11

S90 = 11/2(1080) = 5940 →  sum of all natural numbers which are  divisible by2,9, 5

sum of all natural numbers which are  divisible by 2,9 and 5 = S2+S9+S5-S90 = 250500 +55944 +100500 -5940 = 401004

sum of all natural numbers among the first 1000 numbers = 500500

sum of all natural numbers among the first 1000 numbers which are neither divisible by 2 , 9 and 5 = 500500 - 401004 = 99496