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On Page 11 of Second edition of Concrete Mathematics, it reads as

The induction step has two parts, depending on whether $l$ is even or odd. If $m > 0$ and $2^m + l= 2n$, then $l$ is even and

$J(2^m +l) = 2J(2^{m-1} +l/2)-1 = 2(2l/2+1)-1 = 2l+1$

by (1.8)

Here I didn't get how $2J(2^{m-1} +l/2)-1 $ is reduced to $2(2l/2+1)-1$

Please Help.

MJD
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Brij Raj Kishore
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  • Have you seen mathematical induction before? That's the induction hypothesis in this proof. – MJD Dec 27 '17 at 07:26
  • @MJD I have seen mathematical induction but have done only simpler proofs like sum of natural numbers from Elementry Number theory book by Burton. I think I didn't have deep idea of it – Brij Raj Kishore Dec 27 '17 at 07:30

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