Question

Write the sum using summation notation, assuming the suggested pattern continues.

8 - 40 + 200 - 1000 + ...

Answer 1

Please help me!

Answer 2

Each term differs by a factor of -5:
\[8(5^0)=8\\
8(5^1)=40\\
8(5^2)=200\\\vdots\]Also, each successive term changes sign.
So, using sigma notation, you have
\[\sum_{n=0}^\infty8(-1)^n(5)^n=\sum_{n=0}^\infty8(-5)^n\]

Answer 3

Thank you so very much!