May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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-------------------------------------------------------------COUNTING
~1
7.2
INDUCTION
7.2.1
The
Sum
of
Odd
Numbers
It is time to reconsider one
of
the most important tools in discrete mathematics. We start with a question: we
add
up the first n
odd
numbers. What do we get?
Perhaps the best way to try to find the answer is to experiment.
If
we try small values
of
n, this is what
we find:
=
1 + 3
4
1 + 3 + 5
=
9
1+3+5+7
=
16
1+3+5+7+9
=
25
1+3+5+7+9+11
=
36
1+3+5+7+9+11+13
=
49
1 + 3 + 5 + 7 + 9 +
11
+
13
+
15
64
1 + 3 + 5 + 7 + 9 +
11
+
13
+
15
+
17
=
81
1 + 3 + 5 + 7 + 9 +
11
+
13
+
15
+
17
+
19
=
100
It is easy to observe that we get squares; ...
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