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Find 1_6 + 2_6 + 3_6 + \cdots + 45_6 + 50_6 + 51_6. Express your answer in base 6.

 Jun 4, 2022
 #1
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\(1_6 + 2_6 + 3_6 + \cdots + 45_6 + 50_6 + 51_6 \)

 

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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 Jun 5, 2022

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