The basic idea of mathematical induction is: first, the proposition is correct when n is the initial value (subject n= 1), then it is proved that the proposition is correct when n=k, and then the proposition of n=k+ 1 is also correct. Finally, the conclusion is summarized.

This topic is to prove that the general term of series A 1 = 1/2 and A (n+ 1) = 3an/(an+3) is an=3/(n+5).

First, when n= 1, A 1/2 = 3/ 1+5, a (1+1) = 3 *1/2/(65438+.

Then, let n=k and the proposition is correct, that is, ak=3/(k+5).

Then a (k+1) = 3ak/(AK+3) = 9/(k+5) ÷ [3/(k+5)+3] = 3/(k+6) = 3/[(k+1).

The proposition that ∴n=k+ 1 an=3/(n+5) is also correct.

Finally, an=3/(n+5) is obtained by synthesizing the previous results.