Solve {l}{a_{n}=1/n(n+1)}{n=7/8}

$$\left. \begin{array} { l } { a _ { n } = \frac { 1 } { n ( n + 1 ) } } \\ { n = \frac { 7 } { 8 } } \end{array} \right.$$

Solve for a_n, n

$$a_{n}=\frac{64}{105}\approx 0.60952381$$

$$n=\frac{7}{8}=0.875$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$a_{n}=\frac{1}{\frac{7}{8}\left(\frac{7}{8}+1\right)}$$

Add \frac{7}{8} and 1 to get \frac{15}{8}.

$$a_{n}=\frac{1}{\frac{7}{8}\times \frac{15}{8}}$$

Multiply \frac{7}{8} and \frac{15}{8} to get \frac{105}{64}.

$$a_{n}=\frac{1}{\frac{105}{64}}$$

Divide 1 by \frac{105}{64} by multiplying 1 by the reciprocal of \frac{105}{64}.

$$a_{n}=1\times \frac{64}{105}$$

Multiply 1 and \frac{64}{105} to get \frac{64}{105}.

$$a_{n}=\frac{64}{105}$$

The system is now solved.

$$a_{n}=\frac{64}{105} n=\frac{7}{8}$$