Find \(1_6 + 2_6 + 3_6 + \cdots + 45_6\). Express your answer in base 6.
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
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
\(\displaystyle 2S=50_{6}+50_{6}+50_{6}+\dots +50_{6}=50_{6}\times45_{6}=4010_{6},\\S=4010_{6}/2=2003_{6}.\)
+36916 
