$\large111_2+111_3+111_4+\ldots+111_{16}=\ ?$

Give your answer in decimal representation.

The answer is 1645.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

For any radix $\large r$ , as $\large (111)_r = r^2 + r + 1,$ hence the given summation is $\large \sum_{r = 2}^{16} ( r^2 + r + 1 ) = 1645$ Please see Jake Lai's first three lines for steps to get 1645.