1. Verify that it is satisfied when n= 1.
2. Assume that n=k is true, and then deduce (or fabricate) that n=k+1is also true by using the formulas when n= 1 and n = k.
So it can be concluded that the equation holds.
The way to do this problem is:
1. If n= 1 holds, it means left = 1 and right =1/2 *1* 2 =1.
Left = right, established
2. If n=k, 1+2+3+ holds. . . +k= 1/2*k(k+ 1)
Therefore, when n=k+ 1,
Left = 1+2+3+...+k+k+ 1 = 1/2 * k(k+ 1)+(k+ 1)= 1/2 *。
Therefore, it also holds when n=k+ 1.
From the above, we can draw a conclusion that the original formula is effective.