Question

0.4444 as a geometric series

Answer 1

Expand 0.444… as

0.444… = 4 × 0.111…

0.444… = 4 × (0.1 + 0.01 + 0.001 + …)

0.444… = 4 × (1/10 + 1/100 + 1/1000 + …)

0.444… = 4 × (1/10¹ + 1/10² + 1/10³ + …)

so that

`0.444\ldots = 4 \displaystyle \sum_(n=1)^\infty \frac1{10^n}`