- #1
jonroberts74
- 189
- 0
[tex]1^3+2^3+...+n^3 = \left[ \frac{n(n+1)}{2}\right]^2; n\ge 1[/tex]
[tex]P(1) = 1^3 = \frac{8}{8} = 1[/tex]
[tex]P(k) = 1^3+...+k^3 = \left[ \frac{k(k+1)}{2}\right]^2[/tex] (induction hypothesis)
[tex]P(k+1) = 1^3+...+k^3+(k+1)^3 = \left[\frac{(k+1)(k+2)}{2}\right]^2[/tex]
I start getting stuck here
I foiled it out then let m = P(k)
[tex]\left[ m + \frac{2(k+1)}{2}\right]^2[/tex]
[tex]P(1) = 1^3 = \frac{8}{8} = 1[/tex]
[tex]P(k) = 1^3+...+k^3 = \left[ \frac{k(k+1)}{2}\right]^2[/tex] (induction hypothesis)
[tex]P(k+1) = 1^3+...+k^3+(k+1)^3 = \left[\frac{(k+1)(k+2)}{2}\right]^2[/tex]
I start getting stuck here
I foiled it out then let m = P(k)
[tex]\left[ m + \frac{2(k+1)}{2}\right]^2[/tex]
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