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Asked Oct 15, 2019

Induction proof for part c

Exercise 3: Prove the following statements. I suggest induction.
n(n+1)(2n+ 1)
(a) For all integers n > 0, 12+ 22 ++n2
6
(b) For all n > 0, (1 +2 +...+ n)2 = 13 +23
n3.
(c) For n 2 2, n < (2 - n-1)".
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Exercise 3: Prove the following statements. I suggest induction. n(n+1)(2n+ 1) (a) For all integers n > 0, 12+ 22 ++n2 6 (b) For all n > 0, (1 +2 +...+ n)2 = 13 +23 n3. (c) For n 2 2, n < (2 - n-1)".

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Step 1

Step 2

First prove that the given expression is true for n = 2.

2 2
3
2
2 2.25
V
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2 2 3 2 2 2.25 V

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Step 3

Now assume that the given expression is true for all n = k.

...
k 2
k
..1)
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k 2 k ..1)

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