Write the first five terms of the sequences whose $n^{t h}$ term is:

$a_{n} = \frac{n}{n + 1}$

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Solution

Here, $a_{n} = \frac{n}{n + 1}$

Putting n = 1, 2, 3, 4 and 5, we have

$a_{1} = \frac{1}{1 + 1} = \frac{1}{2} a_{2} = \frac{2}{2 + 1} = \frac{2}{3}$

$a_{3} = \frac{3}{3 + 1} = \frac{3}{4} a_{4} = \frac{4}{4 + 1} = \frac{4}{5}$

$a_{5} = \frac{5}{5 + 1} = \frac{5}{6}$

Thus, the first five terms of sequence are

$\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5} a n d \frac{5}{6} .$

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