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Find \(1_6 + 2_6 + 3_6 + \cdots + 45_6\). Express your answer in base 6.

 Mar 29, 2020
 #1
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Here is one way...convert to base 10....find answer ....then convert to base 6

 

1+2+3+4........+29 = \(\sum_{1}^{29}\) n   = 435      =     20036

 Mar 29, 2020
 #2
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Here's another.

\(\displaystyle S = 1_{6}+2_{6}+3_{6}+\dots+45_{6}.\)

\(\displaystyle S=45_{6}+44_{6}+43_{6}+\dots+1_{6}.\)

Add

\(\displaystyle 2S=50_{6}+50_{6}+50_{6}+\dots +50_{6}=50_{6}\times45_{6}=4010_{6},\\S=4010_{6}/2=2003_{6}.\)

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 Mar 29, 2020

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