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.
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......"?
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!
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).
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.
ur the goat prof kimberly thank you so much for this video
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......"?
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!
thank you very very much for these videos
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).
I'll take another look at that video. Thanks!
you r the best
Great video. Why did you add 2k+1 to both sides?
That is the definition of an odd integer
❤👍
very complex video