Question

consider some integer between 1 and 400. these integer are multiples of 2,3,4,5,6...etc. find the sum of the multiples of 2

Answer 1

first thing to note
we need to find between 1 and 400(so 1 and 400 not included)
multiple of 2 form an AP with difference 2
2,4,6.......398
398=2+(n-1)2
396/2=n-1
198+1=n
199=n
so sum
=199/2(2+198)
=199/2(200)
=199(100)
=19900
Answer = 19900