We can list the sum of the first $n$ consecutive odd positive integers that are less than $40$: \begin{align*}
1&=1, \\
1+3&=4, \\
1+3+5 &= 9, \\
1+3+5+7 &= 16, \\
1+3+5+7+9 &= 25, \\
1+3+5+7+9+11 &= 36.
\end{align*}So, the six consecutive odd positive integers $1,3,5,7,9$, and $11$ can be added together. Since $1+3+5+7+9+11+13 = 49 > 40$, the answer is $\boxed{6}$.
What is the largest number of consecutive odd positive integers that can be added together before the sum exceeds $40$?
1 answer
1 answer