Question

Find the nth term of the sequence
$\frac{1}{2},\frac{2}{3},\frac{3}{4},..........$

Answer 1

In the given sequence is $\frac{1}{2},\frac{2}{3},\frac{3}{4},......$, the first term $t_1=\frac{1}{2}$, second term $t_2=\frac{2}{3}$ and third term $t_3=\frac{3}{4}$.

We observe that:

$t_1=\frac{1}{1+1}=\frac{1}{2}$ and

$t_2=\frac{2}{2+1}=\frac{2}{3}$ and so on...

Therefore, the given sequence is of the form $t_n=\frac{n}{n+1}$.

Hence, the nth term of the sequence is $t_n=\frac{n}{n+1}$.