Obtain-a-general-formula-for-the-sequence-2-3-4-5-8-9-16-17-32-33-assuming-the-sequence-continues-in-that-pattern-

Question Number 165361 by MikeH last updated on 31/Jan/22

Obtain a general formula for

the sequence

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

assuming the sequence continues in that

pattern .

Commented by MJS_new last updated on 31/Jan/22

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

Commented by MJS_new last updated on 31/Jan/22

you can like or dislike it but it still is one

of zillions of right answers

Answered by Rasheed.Sindhi last updated on 31/Jan/22

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

\frac{2}{2 + 1}, \frac{4}{4 + 1}, \frac{8}{8 + 1}, \frac{16}{16 + 1}, \frac{32}{32 + 1}, \dots

\frac{2^{1}}{2^{1} + 1}, \frac{2^{2}}{2^{2} + 1}, \frac{2^{3}}{2^{3} + 1}, \frac{2^{4}}{2^{4} + 1}, \frac{2^{5}}{2^{5} + 1}, \dots, \frac{2^{n}}{2^{n} + 1}