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Quandaries & Queries
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Topic:
inductive
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Proof by induction
2001-10-16
From John:
Can you help me with any of these?
For any natural number n > 1, prove that
(4
n
) / (n + 1) < [(2n)!] / [(n!)
2
].
For any natural number n > 1, prove that
1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) > sqrt(n).
For any natural number n and any x > 0, prove that
x
n
+ x
n - 2
+ x
n - 4
+ ... + x
-n
>= n + 1.
Answered by Penny Nom.
Inductive reasoning pattern
1999-09-13
From Greg Walsh:
What are the next 2 rows of the pattern?
3
13
1113
3113
2123
112213
312213
Answered by Walter Whileley.
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