You should take the sum of I.H (k^2) and substitute that in for 1 + 3 + 5 + … (2k - 1) since we are assuming they equal each other. So you can now do, k^2 + 2k + 1 = (k + 1)^2.
@artemkrazhan8603Ай бұрын
ur the goat prof kimberly thank you so much for this video
@karqoa39682 жыл бұрын
thank you very very much for these videos
@Userpng77y Жыл бұрын
Thanks for the course, but this should be seen according to the roden of the youtube playlist or according to the number of the videos "5.1.1, 5.1.2......"?
@XxNGameCubexX23 күн бұрын
Slight mistake on the well-ordering principle slide, I think the professor meant to say S is a subset of Z+, Q+, or R+, respectively, not element of. Thanks for your lectures!
@AdrianMeyer812 күн бұрын
Very appreciative for making the making these courses available, Kimerbly! But - however I am a bit confused, how does 1 + 3 + 5 + ... + (2k - 1) + (2k +1) = (k + 1)^2? I understand if you would swap "1 + 3 + 5 + ... + (2k - 1)" with the "I.H" witch states "k^2". But teacher in the video doesn't explain this. It would be a lot more time saving if she would adress that when writing 1 + 3 + 5 + ... + (2k - 1) is just the I.H and the I.H is k^2 and next step is to add (2k+1).