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1. When n=1, equation ① is calculated as,
Left Hand Side = 1
Right Hand Side = 1
2. Assuming that n=k is valid,
1 + 3 + 5 + … + (2k-1)=k ②
When n=k+1, the left hand side of ① is written as
1 + 3 + 5 + … + (2k-1)+(2k+1)
=k + (2k+1) (Obtained from equation ①)
=(k+1)
In other words,
1 + 3 + 5 + … + (2k-1)+(2k+1)
=(k+1)
① is valid when n=k+1.
From 1. and 2., equation ① is valid for all ...
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