It is not difficult to create questions like:
Prove by mathematical induction that
for any positive integer .
It is all about the so-called telescoping principle.
What’s it? It’s just one of the methods of finding the sum (or product) of terms.
To evaluate the sum of
it will be easy when we can split each term into
Thus, we may create an m.i. question in the form of
To set up a common M.I. question, just take ‘reasonable’ .
For example, we may take
For the so-called beauty of the question, we may start from k = a, that is
Sum up the above equations, we have
– – – – – – (*)
By putting into (*), we can create the following m.i. questions for students revision:
Prove the following are true for any positive integer ,
3. (The original question above)
Furthermore, if we take
Hence, we have
sum up the above, yields
Thus, we create a question like:
prove by mathematical induction that
for all integers .
Students, try to let other to create some boring m.i. questions at your command.