# Thread: [SOLVED] math induction

1. ## [SOLVED] math induction

can someone help me with this problem? i have to prove that the summation of i^3=(n(n+1)/2)^2

2. Originally Posted by needhelp101
can someone help me with this problem? i have to prove that the summation of i^3=(n(n+1)/2)^2
TO prove with mathematical induction follow these steps

1) Proof for n = 1
Just prove that it is true if we keep the value of n = 1

2)Assume for n= k

Assume that the given statement is correct for n=k
.................................
in your question
Assume
1^3 +2^3 +.....k^3 = (k(k+1)/2)^2

3) Using step 2(the assumption we made) to Prove the statement for n = k+1

...............

in your case prove that

1^3 +2^3 + ....k^3 + (k+1)^3 = ((k+1)(k+2)/2)^2

using
1^3 +2^3 +.....k^3 = (k(k+1)/2)^2-------------(1)

So put (1) in the LHS thus

=(k(k+1)/2)^2 + (k+1)^3

Now simplify this LHS to get $\displaystyle (\frac{(k+1)(k+2)}{2})^2$

3. it was that last part where i'm stuck at. i'm not sure if the [(k+1)(k+2)/2]^2 is the answer.

4. Originally Posted by needhelp101
it was that last part where i'm stuck at. i'm not sure if the [(k+1)(k+2)/2]^2 is the answer.
Do you understand proof by induction? If so, you will appreciate that this result is what step 3 required.

Since this question has been asked and solved in another thread, this thread is closed.