WOLFRAM|DEMONSTRATIONS PROJECT

Sum of Reciprocals of Triangular Numbers

n

2

The sum of the reciprocals of the triangular numbers is

1

1

+

1

3

+

1

6

+...+

1



n+1

2



+⋯=2

.

For each

n

, the area of each colored rectangle in the graphic is

1×

2

n

-

2

n+1

=

1



n+1

2



.