Find the last three digits of the sum of the first 2014 whole numbers.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
The set of whole numbers starts from 0 and consists of all positive integers.
So, the series of the first 2014 whole nos. is : 0 , 1 , 2 , 3 , . . . . . , 2 0 1 3 . Now, we use here the identity 1 + 2 + 3 + . . . . + n = 2 n ( n + 1 )
0 + 1 + 2 + 3 + . . . + 2 0 1 3 = 1 + 2 + 3 + . . . . + 2 0 1 3 = 2 2 0 1 3 × 2 0 1 4 = 2 0 1 3 × 1 0 0 7 = 2 0 2 7 0 9 1
So, the last three digits of the sum is = 0 9 1
Also, you can find the last three digits of the sum by multiplying the numbers formed by the last three digits of 1 0 0 7 and 2 0 1 3 , i.e, by multiplying the numbers 0 0 7 and 0 1 3 and checking the last three digits of that product.
0 0 7 × 0 1 3 = 7 × 1 3 = 9 1 = 0 9 1
So, the last three digits of that product is 0 9 1 , so the last three digits of the original product is also 0 9 1