Question

answer this question​

Answer 1

Answer:

Step-by-step explanation:

We need to find the sum of all the numbers less than 1000, which are neither divisible by 5 nor by 2.

Numbers divisible by 2 upto 1000 are 2, 4 , 6, ........ 1000.

Sum of all the numbers divisible by 2 upto 1000 = 2 + 4 + 6 + ....... + 1000 = 2 (1 + 2 + 3 + .......... + 500)

[Using: sum of first n natural numbers]

Numbers divisible by 5 upto 1000 are 5, 10 , 15, ........ 1000.

Sum of all the numbers divisible by 5 upto 1000 = 5 + 10 + 15 + ....... + 1000 = 5 (1 + 2 + 3 + ........ + 200)

Let us find out the sum of all the numbers which are divisible by both 5 and 2.

Numbers divisible by both 2 and 5 will be divisible by 10.

The numbers upto 1000 which are divisible by 10 are: 10, 20, 30, 40, ............ 990, 1000.

Clearly, this forms an AP with a = 10, d = 10, an = 1000, where n can be found out as follows:

an = a + (n – 1) d

⇒ 1000 = 10 + (n – 1) × 10

⇒n = 100

Sum of all the numbers upto 1000 = 1 + 2 + 3 + ........... + 999 + 1000

Sum of all the numbers less than 1000, which are neither divisible by 5 nor by 2 =

Sum of all the numbers upto 1000 – (Sum of all the numbers divisible by 2 upto 1000 + Sum of all the numbers divisible by 5 upto 1000 – Sum of all the numbers which are divisible by both 2 and 5)

= 500500 – (250500 + 100500 – 50500)

= 200000

Answer 2

hey mate,

the number which is divisible by either 2 or 5 or both is divisible 10 .

that is it must not be divisible by 10.

thus,

the required sum=sum total to 1000-sum of nos. divisible by 10.

[sum of No's. divisible by 10:

1000=10+(n-1)10

990=(n-1)10

n=100

thus,sum=100/2(10+1000)

=50*1010

=5050]

=1000(1000+1)/2 - 5050

=500*1001-5050

=500500-5050

=495450