sum from n=1 to infinity of 5(-1/6)^{5n}

⚠ 5(-1/6)^{5n} is read as 5(-1/6)^(5n): use ^(...) to group an exponent, use * to multiply

Let's calculate:

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

The series is geometric, with first term

- \frac{5}{7776}

and ratio

- \frac{1}{7776}

. Since

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

, its sum is

- \frac{\frac{5}{7776}}{1 + \frac{1}{7776}}

- \frac{\frac{5}{7776}}{1 + \frac{1}{7776}}

- \frac{\frac{5}{7776}}{\frac{7776 + 1}{7776}}

- \frac{\frac{5}{7776}}{\frac{7777}{7776}}

- \frac{5}{7776} \cdot \frac{7776}{7777}

- \frac{38880}{60473952}

The fraction:

\frac{38880}{60473952}

simplifies by the common factor:

7776

into the new fraction:

\frac{5}{7777}

▶Result:

- \frac{5}{7777}

The numeric value of:

- \frac{5}{7777}

is:

▷

\approx -6.4292 \times 10^{- 4}