The Limit of a Sequence with Two Mixed Sums of Arithmetic Sequences
Krystian Karczyński
Founder and General Manager of eTrapez.
Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.
He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.
Sequence limits sometimes use formulas for the sum of arithmetic or geometric sequences. It’s worse if these sequences are given in a “mixed” way in one line, like here:
Example
It’s worth grouping the terms in the denominator differently to notice that there are actually two arithmetic sequences there:
Now we use the formulas for the sum:
And then we just calculate:
Sequence limit calculated 🙂
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