The definition of inverse addition is a classical method to solve the problem of summation of series. It is said that the great mathematician Gauss first used it when he was young. Inspired by this, people created reverse addition. Arithmetic progression's first n terms and formulas are deduced in this way.

If 1+2+3+...+n=?

s = 1+2+3+ 1...+(n- 1)+n

S=n+(n- 1)+...+3+2+ 1

Then 2s = (n+1)+(n+1)+...+(n+1)+(n+1) n.

=n(n+ 1)

So S=n(n+ 1)/2.

Example 2

Find the sum of the first 2n terms of 2462n.

Answer:

2462n

2n2(n- 1)2(n-2)2

Let the sum of the first n terms be s, and the above two expressions are added.

2s =[2+(2n)]+[4+2(n- 1)]+[6+2(n-2)]++[(2n)+2]* * n 2n+2。

Therefore: S=n(2n+2)/2=n(n+ 1).