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Mathematical legal problems
To solve the problem of mathematical induction, its main feature is that the steps are quite fixed:

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.