Question

Why does 6(-5/6)^n converge to zero?

Answer 1

Because the magnitude of -5/6 is less than one.

When two numbers are less than one and repetitively multiplied(like 0.5 to an exponent for instance), they make a smaller and smaller number.

Here is the graph:
http://www.wolframalpha.com/input/?i=6%28-5%2F6%29%5En

Answer 2

I get that (5/6)^n will get smaller and converge to 0. The (-) must make the series alternating. When (5/6)^n converges to zero, it never actually reaches zero. Would one treat it as a 0 being multiplied by 6 anyway when considering infinite behavior?

Answer 3

Yes because even though it is alternating it is getting closer and closer to the x-axis(zero). So (-5/6)^n converges to 0 and 6*0 = 0

Answer 4

Thank you!

Answer 5

No problem