How do I work out an iterative definition (difference equation) for the sequences: (i). {1, 1/4, 1/9, 1/16...} (ii). {3, -6, 12, -24...} Thanks.
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Originally Posted by tkexer How do I work out an iterative definition (difference equation) for the sequences: (i). {1, 1/4, 1/9, 1/16...} (ii). {3, -6, 12, -24...} Thanks. i. The $\displaystyle n$-the term is $\displaystyle 1/n^2$ so: $\displaystyle \frac{1}{(n+1)^2} = \frac{1}{(1+\frac{1}{\sqrt{1/n^2}})^2}$ so: $\displaystyle a_{n+1}=\frac{1}{(1+\frac{1}{\sqrt{a_n}})^2},\ \ \ a_1=1 $ RonL
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