What are the last $1000$ digits of
$$1 + 50 + 50^2 + \dots + 50^{999}$$
when written in base-$10$?
i.e.
What are the last $1000$ digits of
$$ \sum_{k=0}^{999} 50^k$$
Of course, the idea is to find a way to find this manually/mathematically, and only use a calculator/computer if needed.
You don't have to list the $1000$ digits, just some simple, reasonably easy to compute (by a human) description would do too.
[Solution]
$$1 + 50 + 50^2 + \dots + 50^{999}$$
when written in base-$10$?
i.e.
What are the last $1000$ digits of
$$ \sum_{k=0}^{999} 50^k$$
Of course, the idea is to find a way to find this manually/mathematically, and only use a calculator/computer if needed.
You don't have to list the $1000$ digits, just some simple, reasonably easy to compute (by a human) description would do too.
[Solution]
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ReplyDeleteA solution has been posted here: http://ruffnsluff.blogspot.com/2014/10/solution-to-last-1000-digits-puzzle.html
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