The 4th number in the 32nd row of pascals triangle is the sum of how many triangular numbers?

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Answer 1 · 2017-11-05T19:21:22

$30$

First, we must find the fourth number of the thirty-second row of Pascals. That can be found with:

$""_32C_3 = (32*31*30)/(3*2*1)$

However, I won't find the number just yet. In a minute, you'll see why.

Next, we need to know the formula for the sum of triangular numbers. This is:

Now, we need to find a value of $x$ such that:

$(x*(x+1)*(x+2))/6=(32*31*30)/(3*2*1)$

However, I can simply reorder the right hand side to look like this:

$(x*(x+1)*(x+2))/6 =$

$(30*(30+1)*(30+2))/6$

Now, it's easy to notice that $x=30$ .