Question

Write down the sequence if $n$th term is:

a) $\frac{2^n}{n}$

b) $\frac{3+{\left(-1\right)}^n}{3^n}$

Answer 1

a)

$\frac{2^n}{n}$

$=\frac{2^1}{1},\frac{2^2}{2},\frac{2^3}{3},\frac{2^4}{4},.........................,\frac{2^n}{n}$

$=2,2,\frac{8}{3},4,..............,\frac{2^n}{n}$

b)

$\frac{3+(-1{)}^n}{3^n}$

$=\frac{3+(-1{)}^1}{3^1},\frac{3+(-1{)}^2}{3^2},\frac{3+(-1{)}^3}{3^3},\frac{3+(-1{)}^4}{3^4},.........................,\frac{3+(-1{)}^n}{3^n}$

$=\frac{2}{3},\frac{4}{9},\frac{2}{27},\frac{4}{81},........................,\frac{3+(-1{)}^n}{3^n}$