- Thu Dec 12, 2013 4:51 am
- Forum: Advanced Algebra ("pre-calculus")
- Topic: Induction: have a working Proof but first step (n=1) fails
- Replies:
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I am needing to prove the following by induction: {n} {\sum } {\rm }{\rm } 2^{n -1}{\rm } =1+2+2^{2}+...+2^{n -1}=2^{n } {j =0} My proof is like so: A ssumption: 2^{(k-1)} = 2^{k} P roof needed: 2^{(k-1)} + 2^{(k+1-1)} = 2^{(k+1)} Using A ssumption, Added 2^(k+1-1) to both sides: 2^{(k-1)} + 2^{k} =...