Quandaries
and Queries 

Name: Dane


Hi Dane, That's a really nice observation. One of the facts about the number e is that the sequence
approaches e. That is
Some authors take this fact as the definition of e and some authors define e some other way and then prove this fact as a theorem. Your sequence is (almost) every tenth term of the sequence (1 + ^{1}/_{n})^{n}. Your sequence is (1 + ^{1}/_{n})^{n+1} where n is 10, 100, 1000, ... Since the sequence (1 + ^{1}/_{n})^{n} approaches e, the subsequence of every tenth term approaches e also. You multiply the terms of this sequence by the sequence (1+ ^{1}/_{n}). But the limit of the sequence (1+ ^{1}/_{n}) is 1 and hence the limit of your sequence is 1e = e. Penny 

