Is there any particular rule to solve Inductive Step in the mathematical Induction?

In the Inductive Step, we suppose that the result is also true for other integral values k. If the result is true for n = k, then it must be true for other integer value k +1 otherwise the statement cannot be true.

In proving the result for n = k +1, the procedure changes, as it depends on the shape of the given statement.

Following steps are main:

1)      You should simply replace n by k+1 in the left side of the statement.

2)      Use the supposition of n = k in it.

3)      Then you have to simplify it to get right side of the statement. This is the step,

where students usually feel difficulty.

Here sometimes, you have to open the brackets, or add or subtract some terms

or take some term common etc. This step of simplification to get right side of the given statement for n = n + 1 changes from question to question.

 Now check this step in the examples of the Lessons 23 and 24.