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Numerade Educator

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Problem 26 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = 2 + (0.86)^n $

Answer

The sequence converges to 2

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Video Transcript

in order to determine whether or not sequence converges or diverges. I need to figure out whether or not the limited n goes to infinity of a M is some finite number. So this is Lim as n goes to infinity of two. Plus you're a point eight six to the end and since you're a point eight six is less than one and absolute value, which is to say that it's trapped between minus one and one. We know that has end goes to infinity. You're a point eight six to the end is going to go to zero, which means that this limit is going to go to two. So the limit exists and the limit is just some finite number. So it converges two, two.