How do you find the partial sum of Sigma (250-8/3i) from i=1 to 60?

2 Answers
Jan 4, 2018

The answer is 10120 (see below).

Explanation:

First, the commutative and distributive properties allow us to write:

sum_{i=1}^{60}(250-8/3 i)=sum_{i=1}^{60}250-8/3 sum_{i=1}^{60}i.

Now sum_{i=1}^{60}250 is just 250 added to itself 60 times. Therefore sum_{i=1}^{60}250=60*250=15000.

Next, we can use the well-known formula for the sum of the first n integers (see https://brilliant.org/wiki/sum-of-n-n2-or-n3/), which is sum_{i=1}^{n}i=1+2+3+cdots+n=(n(n+1))/2, to say

sum_{i=1}^{60}i=(60*61)/2=30*61=1830.

Hence, the answer is

sum_{i=1}^{60}250-8/3 sum_{i=1}^{60}i

=15000-8/3 * 1830=15000-4880=10120.

Jan 4, 2018

10120

Explanation:

sum_{i=1}^60 (250-8/3*i)=250*60-8/3*(60*61)/2=10120