Proof and Reasoning (Lesson 1/1)
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Discussion
Consider the sum 1+3+5+⋯+(2n−1).
This is what we call a conjecture - basically an informed guess about some pattern that we see sometimes holds.
(a)
Evaluate the sum in the case n=3,4,5.
Solution:
Compute directly by adding the first few odd numbers.
For n=3:
For n=4:
For n=5:
So the sums are 9,16,25 respectively.