SOLUTION: Let Tn be the nth triangular number, Qn be the nth square number and Pn be the nth pentagonal number. (a) Show that 3 Pn= T 3n-1 (b) Show that Pn-Qn = Tn-1 and hence that P3n-3Pn

Algebra ->  Finance -> SOLUTION: Let Tn be the nth triangular number, Qn be the nth square number and Pn be the nth pentagonal number. (a) Show that 3 Pn= T 3n-1 (b) Show that Pn-Qn = Tn-1 and hence that P3n-3Pn      Log On


   

Question 1182883: Let Tn be the nth triangular number, Qn be the nth square number and Pn be the nth pentagonal number.
(a) Show that 3 Pn= T 3n-1
(b) Show that Pn-Qn = Tn-1 and hence that P3n-3Pn= Q3n
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
T%5Bn%5D+=+C%5B2%5D%5E%28n%2B1%29+=+%28n%28n%2B1%29%29%2F2
Q%5Bn%5D+=+n%5E2
P%5Bn%5D+=+%283n%5E2-n%29%2F2
(a)
(b)
===> P%5B3n%5D+-+Q%5B3n%5D+=+T%5B3n-1%5D
===> P%5B3n%5D+-+T%5B3n-1%5D+=+Q%5B3n%5D
Therefore, P%5B3n%5D+-+3P%5Bn%5D+=+Q%5B3n%5D , from part (a).