Question 1093613
sigma sign (up=n, down=(k=0))2^n =2^(n+1)-1
1st:: Show it is true for k = 0
2^0 = 2^(0+1)-1
1 = 2*1-1
1 = 1
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2nd:: Assume it is true for n = k::
2^k = 2^(k+1)-1
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3rd:: Show that it is true for n = k+1::
2^(k+1) = 2*2^k = 2[2^(k+1)-1] = 2^(k+2)-2 = 2^[(k+1)+1]-2
Note:: It is not true in general::
E.G.:: not true for n = 1
2^1 = 2^(1+1)-1
2 = 2^2-1
2 = 3 
Is not true
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Cheers,
Stan H.
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