## Sequence 91, 8911, 889111, 88891111, …

Show that the sequence   $91, \; 8911, \; 889111, \; 88891111, \; ...$
(putting one more 8 on the front and one more 1 on the end)
consists solely of triangular numbers:

$91 \; = \; T_{13}$
$8911 \; = \; T_{133}$
$889111 \; = \; T_{1333}$
$88891111 \; = \; T_{13333}$
…………………………..
…………………………..