Proof:

> 1

= 1 + a_n for each n > 1 Hence, we can raise both sides to the n-th power and use the Binomial theorem:

In particular, since all terms are positive, we obtain

Solving this for a_n we obtain

0 a_n

But that implies that a_n converges to zero as n approaches to infinity, which means, by the definition of a_n that converges to 1 as n goes to infinity. That is what we wanted to prove.

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Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007