Question

Find the sum a+(a+1)+(a+2)+…….(a+n-1) in terms of a and n

Answer 1

n!*a + (n-1)!

Answer 2

no way any factorials could be involved in such a sum

There are n terms, so we have

na + 0+1+2+...+(n-1)

We all know the sum of the first n-1 integers is (n-1)n/2, so the final sum is

na + n(n-1)/2 = n(a+n-1)/2