Evaluate the following series

Question

 

⁴∑_k=0  -6^k

Answer 1

The sum = -(1+6+6^2+6^3+6^4)

Answer 2

Hi, Grace.

This notation means the sum of all numbers -6^k when k=0, 1, 2, 3, and 4.

 = -6⁰ - 6¹ - 6² - 6³ - 6⁴                     (since the -6 is not in paretheses, all values are negative)

 = -1 - 6 - 36 - 216 - 1296

 = -1555

Hope this helps!

Answer 3

Recall aΣ_k=0...n b^k = a(b^k+1-1)/(b-1)

Here we have a=1, b=-6, and n=4 so the sum is ((-6)⁵-1)/(-6-1) = (-7777)/(-7) = 1111

Or you can just add up the terms since there are just 5:

1 - 6 + 36 - 216 + 1296 = 1111