If N = 0.369369369369… and M = 0.531531531531…, then what is the value of (1/N) + (1/M)?
11100/2419
Convert recurring decimals to fractions:
\[N=\frac{369}{999}=\frac{41}{111},\quad M=\frac{531}{999}=\frac{59}{111}\]
Therefore \(\frac{1}{N}=\frac{111}{41}\) and \(\frac{1}{M}=\frac{111}{59}\).
\[\frac{1}{N}+\frac{1}{M}=\frac{111\times 59+111\times 41}{41\times 59}=\frac{111\times 100}{2419}=\frac{11100}{2419}\]
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