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Roscoe1989
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1. can someone tell me what r^(n+1)*(1-r)=? I need it to solve a proof, but my math is so rusty! thanks!
2. r^(n+1)*(1-r)
2. r^(n+1)*(1-r)
Roscoe1989 said:oopps, sorry. it should be
1+r+...+r^n=1-r^(n+1) / 1-r
Roscoe1989 said:my textbook is saying 1-r^n+1
Roscoe1989 said:my textbook is saying 1-r^n+1
Roscoe1989 said:is it n can't be 0? but can be anything else?
Roscoe1989 said:n has to be greater than 0
Roscoe1989 said:then the right hand side will equal 1. right?
flyingpig said:Why?
Dick said:Why not? I would interpret 1+r+...+r^n for n=0 to be 1. (1-r^(0+1))/(1-r)=(1-r)/(1-r)=1. I'm not sure you are leading this in a helpful direction, flyingpig.
Roscoe1989 said:honestly, i don't know
Roscoe1989 said:does it mean that it's "proven"?
flyingpig said:By Induction? No
If only though, if only...
Roscoe1989 said:but what does it mean on the LHS?
Dick said:You don't really need induction for an informal proof. See my long buried comment in post 14.
Roscoe1989 said:prove by induction on n that
1+r+r^2...+r^=1-r^n+1/1-r
if r doesn't equal 1