[SOLVED] Proof by induction help needed (urgently)

May 2009
72
21
Brooklyn, NY
...
I just dont get how 3^k + 0.5(3^k -1) becomes 0.5(3^k+1 -1)

Thanks
Simplify the expression: \(\displaystyle 3^k + \frac{1}{2} 3^k - \frac{1}{2}\)
 

suf

Jun 2010
3
0
Thats what im having probelms with
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
Simplify the expression: \(\displaystyle 3^k + \frac{1}{2} 3^k - \frac{1}{2}\)
\(\displaystyle 3^k + \frac{1}{2}\cdot 3^k - \frac{1}{2} = \left(1 + \frac{1}{2}\right)3^k - \frac{1}{2}\)

\(\displaystyle = \frac{3}{2}\cdot 3^k - \frac{1}{2}\)

\(\displaystyle = \frac{1}{2}\cdot 3^{k + 1} - \frac{1}{2}\)

\(\displaystyle = \frac{1}{2}(3^k - 1)\).
 
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