Mathematics
Hannah02
7

How do I prove that 1+r+r^2+r^3+r^4+r^5=(1-r^6)/(1-r) ?

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(1) Answers
katiebabyyy

let's say [latex]A=1+r+r^2+r^3+r^4+r^5[/latex] let's multiple all member by r [latex]r*A=r+r^2+r^3+r^4+r^5+r^6[/latex] Now we subtract [latex]A-r*A=(1+r+r^2+r^3+r^4+r^5)-(r+r^2+r^3+r^4+r^5+r^6)[/latex] [latex]A-r*A=1+r+r^2+r^3+r^4+r^5-r-r^2-r^3-r^4-r^5-r^6[/latex] [latex]A(1-r)=1-r^6[/latex] therefore... [latex]\boxed{\boxed{\boxed{\therefore~A=\frac{(1-r^6)}{(1-r)}}}}[/latex]

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