Sierpinski Triangle

Number Theory Level 3

$\large \displaystyle \sum_{n=1}^\infty \frac{ \prod_{k=0}^{n} ({n \choose k} \mod 2)}{n+1} = \, ?$

1 solution

Michael Mendrin
Aug 18, 2016

NIcholas, if you don't mind, I've fixed your problem, changing from $n=0$ to $n=1$ in the summation. Otherwise, the answer would have been $2$ .

By the way, it looks like you're pretty close to one of the homes I live in. Hi, neighbor, how's it going?

Thank you very much. I just noticed that as well.

Nicholas Stearns - 4 years, 10 months ago

I answered 2. Isn't it the right answer?

Hana Wehbi - 4 years, 10 months ago

Originally it was, when the summation was marked as $n=0$ , which would have added $1$ to the rest of the sum. Slight oversight.

Michael Mendrin - 4 years, 9 months ago

Thank you.

Hana Wehbi - 4 years, 9 months ago