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Show that 3tn+ tn−1= t2n, where tn is the nth triangular number.

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Show that 3tn+ tn−1= t2n, where tn is the nth...

Numbers Theory

numbers theory

asked Mar 9, 2013 in Algebra 1 Answers by anonymous

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1 Answer

t_n=n(n+1)/2 by definition.

3t_n+t_n-1=3n(n+1)/2+n(n-1)/2=

(3n²+3n+n²-n)/2=(4n²+2n)/2=

2n²+n=n(2n+1)=2n(2n+1)/2=t_2nQED

answered Jun 8, 2022 by Rod Top Rated User (1.2m points)

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