How do you write the first six terms of the sequence $a_{n} = \frac{n}{n + 1}$ $a_n=n/(n+1)$ ?

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Answer 1 · 2016-10-21T16:03:07

The $n$ $n$ subscript tells us which term of the sequence it is.

so $u_{1}$ $u_1$ is the first term so $n = 1$ $n=1$ and we substitute $n = 1$ $n=1$ into the expression. $u_{2},$ $u_2,$ is when $n = 2$ $n=2$ etc.

we have therefore:

$a_{n} = \frac{n}{n + 1}$ $a_n=n/(n+1)$

$a_{1} = \frac{1}{1 + 1} = \frac{1}{2}$ $a_1=1/(1+1)=1/2$

$a_{2} = \frac{2}{2 + 1} = \frac{2}{3}$ $a_2=2/(2+1)=2/3$

$a_{3} = \frac{3}{3 + 1} = \frac{3}{4}$ $a_3=3/(3+1)=3/4$

$a_{4} = \frac{4}{4 + 1} = \frac{4}{5}$ $a_4=4/(4+1)=4/5$

$a_{5} = \frac{5}{5 + 1} = \frac{5}{6}$ $a_5=5/(5+1)=5/6$

$a_{6} = \frac{6}{6 + 1} = \frac{6}{7}$ $a_6=6/(6+1)=6/7$

How do you write the first six terms of the sequence a_n=n/(n+1)an=nn+1a_n=n/(n+1)?