Question

1. What is the sum of the series?
2. What is the sum of the series?

Answer 1

1).90

2).-10

Explanation:

1).

(3(1)^2)+(3(2)^2)+(3(3)^2)+(3(4)^2)

3 + 12 + 27 + 48

=90

2). (-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)

(-15+20) + (-20+20) + (-25+20) + (-30+20)

5 + 0 + -5 + -10

=-10

Answer 2

So for finite series like these, you just plug in each number for k that it tells you. The first says the sum of 3k^2 from k=1 to k=4. Just plug integer k between 1 and 4 into the equation and add them together:

3(1^2)+3(2^2)+3(3^2)+3(4^2)=90

Same for the next one, except this is for all values of k between 3 and 6:
(-5(3)+20)+(-5(4)+20)+(-5(5)+20)+(-5(6)+20)=-10