what is a triangular number ?

• Oct 14th 2008, 01:19 PM
sportychick1912
what is a triangular number ?
what is a triangular number ????
• Oct 14th 2008, 01:24 PM
vincisonfire
A triangular number is the sum of the n natural numbers from 1 to n. The sequence of triangular numbers for n = 1, 2, 3... is: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ....
• Oct 14th 2008, 01:42 PM
Soroban
Hello, sportychick1912!

Quote:

What is a triangular number?

They arise from triangular arrays of objects.
Code:

                                              o                                 o          o o                       o        o o        o o o             o      o o      o o o      o o o o       o    o o    o o o    o o o o    o o o o o       1      3        6        10          15

And we have:

. . $\begin{array}{ccccc}T_1 &=& 1 &=& 1 \\
T_2 &=& 1+2 &=& 3 \\ T_3 &=&1+2+3 &=& 6 \\ T_4 &=&1+2+3+4 &=&10 \\ T_5 &=& 1+2+3+4+5 &=&15 \\ \vdots & & \vdots & & \vdots \\
T_n &=& 1+2+3+\hdots+n &=&\dfrac{n(n+1)}{2}\end{array}$