• anonymous
Consider the sequence $$a_n$$ whose $$n$$th term is given by the reciprocal of the first digit of $$n!$$. For example, $$a_1=1$$ since the first digit of $$1!=1$$ is $$1$$; $$a_6=\dfrac{1}{7}$$ since $$6!=720$$, and so on. Take another sequence, $$b_n$$, a subsequence of $$a_n$$ that doesn't contain $$1$$. (This measure is taken just in case there are infinitely many terms of $$a_n$$ that are $$1$$.) Does $$\displaystyle\sum_{n=1}^\infty b_n$$ converge?
Calculus1

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