Question

How do you add these two consecutive triangular numbers?
TR(4)+TR(3)

Answer 1

The n-th trianglar number is given by

`T_n = \frac{n(n+1)}2`

Then

`T_4 + T_3 = \frac{4*5}2 + \frac{3*4}2 = \boxed{16}`

Alternatively, the triangular numbers are defined recursively by

`\begin{cases}T_1 = 1 \\ T_n = T_(n-1) + n & \text{for } n>1\end{cases}`

This means

`T_1=1`

`T_2 = T_1 + 2 = 3`

`T_3 = T_2 + 3 = 6`

`T_4 = T_3 + 4 = 10`

so that

`T_3+T_4=\boxed{16}`