Find 1_6 + 2_6 + 3_6 + \cdots + 45_6 + 50_6 + 51_6. Express your answer in base 6.
+118608 \(1_6 + 2_6 + 3_6 + \cdots + 45_6 + 50_6 + 51_6 \)
Probably the most straight forward way to takle this problem is to work out what 51 base 6 is in base 10,
do the sum and then convert back.
51base6 = 5*6+1 = 31 base 10
1+2+...+31 = 31/2(2+30)= 31*16 = 496
496/6 = 82R4
82/6=13R4
13/6=2R1
2/6=0R2
496 base 10 = 2144 base6
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I just want to play with another method (all working is in base 6)
(0+ 1+2+3+4+5) + ( 10+ .... 15) + ( 20 .....+25 ) + ( 30 ....+35 ) + ( 40+....45 )+ 50 +51
= 5(0+1+2+3+4+5) +0+1 + (10*10) + (20*10) +(30*10) + (40*10) +50*2
= 5* (10+10+3) +1 + 100 + 200 + 300 + 400 + 140
= 5* 23 +1 + 1540
= 204 +1540
= 2144 base 6
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