Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I have to prove the following by induction for all of n which are elements of N:

1^3 + 2^3 + ... n^3 = 1/4 * n^2 * (n + 1)^2

Now, I have never been successful at proofs, much less proofs by induction. And I never have really had any formal instruction on how to construct a proof by induction. So I could use all the help I can get.

NOTE: I do NOT want someone to give me an answer. I would rather someone guide me to an answer illustrating a formal method of constructing a proof by induction (with anotations on the side if possible). [?]

BTW, I am using "Schaum's Outlines: Modern Abstract Algebra". And my question is in Chapter 3: Natural Numbers, page 37, 25 c).

I know this is a tall order, but if anyone cares to spend the time to teach, I will most certainly spend the time to learn.

Here is my work so far. Note: Although I may have some steps in the proper order, and it may seem like I know what I am doing, I really do not. That is, I don't know the reasoning behind every step that I do and why it is in the format that it is. That being said, onto the proof.

Propostition:

== state the proposition

P(n): 1^3 + 2^3 + ... n^3 = 1/4 * n^2 * (n + 1)^2

for every n which is an element of N (the set of Natural numbers).

Base Case: P(1)

== show that the proposition holds for the first element in the set.

1^3 = 1/4 * 1^2 * (1 + 1)^2

1 = 1

So P(1) is true.

Inductive Case:

== show that if the proposition holds for an element k, it should hold for it's successor.

If P(k) is true then P(k+1) must be also true.

(Here is where I am definitely in the dark on how to proceed).

Any help is appreciated. BTW, how is the proof so far? Am I interpreting it correctly? And is my format sound?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof by Induction

**Physics Forums | Science Articles, Homework Help, Discussion**