How is ( 10 4 ) 6 − 1 10 4 − 1 = 1 + 10 4 + 10 8 + 10 12 + 10 16 + 10 20 ?

Question

How is             (              10                  4                            )                  6                    −      1                      10        4            −      1        =  1  +      10          4        +      10          8        +      10          12        +      10          16        +      10          20      ?

Samuel Vang · Accepted Answer

Note that for   x  ≠  1,   (  x  −  1  )  (      x    5    +      x    4    +      x    3    +      x    2    +  x  +  1  )  =      x    6    −  1  ⇒                    x        6            −      1              x      −      1        =      x    5    +      x    4    +      x    3    +      x    2    +  x  +  1

Kellen Perkins · Accepted Answer

It is true in general that       x    6    −  1  =  (  x  −  1  )  (  1  +  x  +      x    2    +  ⋯  +      x    5    ). Just substitute   x  =      10    4

How is ( 10 <mrow class="MJX-TeXAtom-ORD"> 4

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