Question

How do i use gauss’s approach to find the sum of 8+ 14+ 20+26+…..+62

Answer 1

Gauss's approach consists of a method to find the sum of the first N natural numbers:

$1+2+\cdots+(N-1)+N=\frac{N\cdot(N+1)}{2}\text{.}$

1) To use Gauss's approach, we write the sum of the problem as:

$\begin{gathered} 8+14+20+26+\cdots+62 \\ =2\cdot4+2\cdot7+2\cdot10+2\cdot13+\cdots+2\cdot31 \\ =2\cdot(4+7+10+13+\cdots+31) \end{gathered}$

2) Now, we