How much does the number $542$ increase when we merge $ n $ zeros between $ 5 $ and $ 4 $?
I found it out $500\cdot99...9$ (''n'' noves) units
[exemple: $500\cdot9+542=5042$]
But how do I prove it?
2026-03-28 20:56:47.1774731407
Placing $n$ zeroes between $5$ and $4$
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Your original number is $5\cdot 10^2+42$. If you put in $n$ zeros you get $5 \cdot 10^{2+n}+42$. The difference of these is $5 \cdot (10^{2+n}-10^2)=5\cdot 10^2\cdot (10^n-1)$ and the last number consists of $n\ 9$s