Question 1104281
Use Mathematical Induction to show that the following statement is true for all natural numbers n:  1^3+2^3+3^3+...+ n^3 = n^2(n+1)^2/(4)
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Show it is true for n = 1::
1^3 = [1^2(1+1)^2]/4 = (1*2^2)/4 
1 = 4/4
1 = 1
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Assume it is true for n = k,
 1^3 + 2^3 + ... + k^3 = [k^2(k+1)^2]/4
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Show it is true for n = k+1
1^3 + 2^3 + ..+ k^3 + (k+1)^3 = [k^2(k+1)^2]/4 + (k+1)^3
Factor to getl::
= (k+1)^2[k^2/4 + (k+1)]
= (k+1)^2[(k^2 + 4k+ 4)]/4
= (k+1)^2[((k+1)+1)^2]/4
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So it is true for n = k+1.
Cheers,
Stan H.
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