Mathematical Induction ( incl. Step-By-Step Guide and Examples ) - Logic

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This video is about Mathematical Induction; a mathematical proof technique.
In the video the following concepts are explained:
- Mathematical Induction.
- The requirements ( the Well-Ordering property).
- The (well-known) comparison with dominoes.
- A step-by-step guide on how to prove statements using mathematical induction.
- Two exercises (involving a summation and a factorial).
We solve the following two exercises:
- For all n in the natural numbers: the sum from i=1 to n over 2^i = 2^(n+1) - 2.
- For all n in the natural numbers: the sum from i=1 to n over i(i!) = (n+1)! - 1.
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This video has been published by MisterCode.

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Hi!, How is (k+1)*(k+1)! + (k+1)! - 1 converted to (k+2)*(k+1)! - 1? Thanks,