find-an-explicit-formula-for-the-sequence-2-3-4-5-8-9-16-17-32-33-

Question Number 159222 by physicstutes last updated on 14/Nov/21

find an explicit formula for

the sequence

\frac{2}{3}, \frac{4}{5}, \frac{8}{9}, \frac{16}{17}, \frac{32}{33}, \dots

Commented by MJS_new last updated on 14/Nov/21

a_{n} = 1 - \frac{12}{n^{4} - 6 n^{3} + 23 n^{2} - 18 n + 36}

a_{n} = \frac{7}{33660} n^{4} - \frac{13}{16830} n^{3} - \frac{767}{33660} n^{2} + \frac{3433}{16830} n + \frac{818}{1683}

\dots

Answered by TheSupreme last updated on 14/Nov/21

a_{n} = \frac{2^{n}}{2^{n} + 1} i s o n e o f t h e i n f i n i t e s o l u t i o n s