Sequences, Series, and Credit Card Fees

[mathjax] If you're like me, you may have suffered through sequences and series in Calculus class with amazement: it makes sense, but how did anyone come up with this in the first place? Why would they think to even do this? Clearly smarter people exist in the world to bring such strange things to us. But I was looking at this problem recently... A customer with a large invoice (let's say, \$1000) wants to pay with a credit card -- but credit cards charge serious merchant fees, a percentage of the total billed amount. So, for that \$1000 charge, the credit card company might take 3%, or \$30. At larger dollar amounts or over many transactions, this can take a serious chunk out of revenue. Since credit cards are offered…
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