Discrete math-Mathematical induction

Question

Hello there,

I was just wondering my lecturer deduct my marks for this and gave 1/2 out of 2:

Given 4+8+12+...+4n = 2n^2+2n for n>=1,

My solution: 1. Inductive base: n =1, 4 = 4;

2. Hypothesis: Assume n=k, for k>=1;

3. Step:  n = k+1

4+8+12+...+4k+4(k+1)   =       2(k+1)^2 + 2(k+1)

2k^2+2k+4k+4               =        2(k+1)^2 + 2(k+1)

2k^2+4k+2+2k+2           =        2(k+1)^2 + 2(k+1)

2(k+1)^2 + 2(k+1)          =        2(k+1)^2 + 2(k+1), Hence n = k+1 is true.

 

Is there something wrong with this? 

Lecturer told me that I have to follow his style of writing and did not even consider of me doing this way telling me it is wrong.

Can someone tell me what is wrong?

 

 

Answer 1

4+8+12+...+4n=2n^2+2n for n>=1

my step 3 would be:

4+8+12+...+4k+4(k+1)=2(k+1)^2+2(k+1)

                                    =2k^2+4k+2+2k+2

                                    =2k^2+2k+4k+4 (rearrange the terms and add the 2's together)

                                    =(2k^2+2k)+4(k+1)

                                     substitute from the original equation (n=k)

                                    =(4+8+12+...+4k)+4(k+1) which is the left side of the equation right under "my step 3"