Any tips on how to conjecture formulas for Induction?

[phillyolly]

What are usual tips in conjecturing formulas for math induction if I am given a certain sum of sequence? Thank you.

 

[╔(σ_σ)╝]

It depends on the problem.

In the case of sums...

Sometimes simply reversing the order and adding it to itself and then grouping terms is sufficient.

In the case of the geometric series simply multipliying the partial sum by the "r" of the geometric series and then performing S-rS can do some magic.

Usually there is some sort or clever trick involved and no one can really give you a procedure for coming up with clever tricks.

I only "general" way of coming up with formulas of that sort is generatingfunctionology ,yes it is actually a topic. I remember coming across an online book of that sort when I wanted to find a solution to a recursive integral. I didn't have the patience to read through more than 5pages though.