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Exercise 5
Math Animated™
Mathematical Introduction for Physics and Engineering
by Samuel Dagan (Copyright © 2007-2020)
Chapter 1: Differentiation; Section 1: Real Numbers; page 2
Operations, Exercise 5
Question
Prove by induction that :
Part 1
For n=1 we have
that is correct
Part 2
By assuming that the given relation for n is correct, one is required to obtain the relation for n+1 . We have to prove that:
Part 3
The lefthand side of part 2 gives:
which is exactly equal to the righthand side of part 2.
Score
Part 1 is worth 3 points, zero if wrong or missing.
Part 2 is worth 5 points, zero if wrong or missing.
Part 3 is worth 2 points, zero if wrong or missing.