Induction Q (1 Viewer)

Drewk · Nov 26, 2012

Prove by Induction
n * 2^n-1 = (n-1)2^n for all n=>1
Here is my current working, could you please advise on what i am doing wrong or how i can make LHS=RHS(continue from my last line)
http://snag.gy/rejma.jpg

Shadowdude · Nov 26, 2012

Your working... assumes the answer.

Your first line in (3) is like "these two things are equal". That's not true. You want to show these things are equal.

Your working should go:

$k.2^{k+1} + (k+1)2^{(k+1)-1} = \left (1 + (k-1)2^{k} \right ) + (k+1)2^{k}$ (by inductive assumption)

$1 + (k-1)2^{k} + (k+1)2^{k} = 1 + k2^{k} - 2^{k} + k2^{k} + 2^{k} = 1 + 2k2^{k} = 1 + k.2^{k}.2^{1} = 1 + k2^{k+1} \square$

which is what you want, the RHS of your first line in (3).

Induction Q (1 Viewer)

Drewk

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Shadowdude

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