Question

Find the sum of all positive integers less than 1000 that are not multiple of 3

Answer 1

Answer:

You want to calculate the sum

S=∑999n=1n−∑333n=13n

Let N=999 , M=333 . Using the known formula for the sum of positive integers up to N you reach

S=N(N+1)2−3M(M+1)2

Step-by-step explanation:

it is not too hard but not very easy.

Mark as brinlist guy's

Answer 2

Step-by-step explanation:

Note

∑k=1nk=

1+2+3+…+n=

n2+n2=

n(n+1)2=

n2⋅(n+1)=

n⋅n+12

1000=3⋅333+1

thus the sum of all positive integers less than 1 000 is 1+2+3+…+999=999⋅500=499 500

and the sum of all positive integers less than 1 000 that are multiples of 3 is

3⋅(1+2+3+…+333)=3⋅333⋅167=999⋅167=166 833

the sum you are interested in is the difference of the two:

1+2+4+5+7+…+998=

(1+2+3+…+999)−(3+6+9+…+999)=

(1+2+3+…+999)−3(1+2+3+…+333)=

499 500−166 833=

999⋅500−999⋅167=

999⋅(500−167)=

999⋅333=

3⋅3332=

332 667