sum((-1/6)^(5*n),n=0,+inf) — step-by-step solution

Let's calculate:

\sum_{n = 0}^{+∞} {(- \frac{1}{6})}^{5 n}

The series is geometric, with first term

1

and ratio

- \frac{1}{7776}

. Since

| - \frac{1}{7776} | < 1

, its sum is

\frac{1}{1 + \frac{1}{7776}}

ⅰ

\sum_{n = 0}^{+∞} {(- \frac{1}{6})}^{5 n}

\frac{1}{1 + \frac{1}{7776}}

\frac{1}{1 + \frac{1}{7776}}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

1 + \frac{1}{7776}

\frac{7776 + 1}{7776}

\frac{1}{\frac{7776 + 1}{7776}}

ⓘ The numerator and the denominator are computed before the division:

7776 + 1

7777

\frac{1}{\frac{7777}{7776}}

ⓘ Dividing is multiplying by the reciprocal:

\frac{1}{\frac{7777}{7776}}

\frac{7776}{7777}

▶Result:

\frac{7776}{7777}

The numeric value of:

\frac{7776}{7777}

is:

▷

\approx 0.9999