Number times Recurring Part of Reciprocal gives 9-Repdigit/Examples/41

Example of Use of Number times Recurring Part of Reciprocal gives 9-Repdigit

\(\ds \dfrac 1 {41}\)

\(=\)

\(\ds 0 \cdotp \dot 0 243 \dot 9\)

\(\ds 2439 \times 41\)

\(=\)

\(\ds 10^5 - 1\)

Proof

Let $x = \dfrac 1 {41} = 0 \cdotp \dot 0 243 \dot 9$.

Then $n = 41$; $m = 2439$ and $d = 5$

Therefore:

$2439 \times 41 = 10^5 - 1$

$\blacksquare$