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}
…………………………..
…………………………..

 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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