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|dw:1343194234112:dw|

fundamental theorem of algebra

n=1 is the base case

@experimentX 1 is the base case but it also has to be proved first.

in your formula n-1 > 0, but n-1 =0 for n=1

|dw:1343194693791:dw|

@experimentX is that the final step?

no .. not really,
currently, i cannot think using induction.

no it's purely based on induction.....

it proves directly using geometric sum

u prove very dumb things using induction/by contradiction...........

so now by induction.....we have
xn−yn=(x−y)(xn−1+xn−2y+.....+xyn−2+yn−1 by induction

nd we need to prove
xn+1−yn+1=(x−y)(xn+xny+.....+xyn-1+yn......

so try showing that
(x−y)(xn+xny+.....+xyn-1+yn...... = xn+1−yn+1

|dw:1343195660262:dw|
i guess ... certainly, other ways are more intuitive