The Limit of a Sequence with Two Mixed Sums of Arithmetic Sequences

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 🙂

Krystian Karczyński

Założyciel i szef serwisu eTrapez.

Magister matematyki Politechniki Poznańskiej. Korepetytor matematyki z wieloletnim stażem. Twórca pierwszych Kursów eTrapez, które zdobyły ogromną popularność wśród studentów w całej Polsce.

Mieszka w Szczecinie. Lubi spacery po lesie, plażowanie i kajaki.

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