Question

Write the first five terms of the sequence, whose $n^{th}$ term is $a_n=\frac{n}{n+1}$.

Answer 1

Finding sequence.
Given, $a_n=\frac{n}{n+1},n\in N$
Substituing $n=1,2,3,4$ and $5$ in $a_n$, we get
$a_1=\frac{1}{1+1}\Rightarrow a_1=\frac{1}{2}$
$a_2=\frac{2}{2+1}\Rightarrow a_2=\frac{2}{3}$
$a_3=\frac{3}{3+1}\Rightarrow a_3=\frac{3}{4}$
$a_4=\frac{4}{4+1}\Rightarrow a_4=\frac{4}{5}$ ;
$a_5=\frac{5}{5+1}\Rightarrow a_5=\frac{5}{6}$

Hence, the first five terms of sequence are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}$ and $\frac{5}{6}$.