how do you get this problem $\displaystyle [k(k+1)/2]^2 + (k+1)^3$ down to $\displaystyle [(k+1)(k+2)/2]^2$ I'm having troubles with the arithmetic...
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Wait, is this true? Factor $\displaystyle (k+2)^2$ out to get $\displaystyle (k+1)^2\left(\frac{k}{2}+(k+1)\right)$. Then combine the terms by getting a common denominator. But, it doesn't seem to give you what claim it does.
Yeah I don't get this one either =/
so i factored out (k+1)^2 and i got this....1/4(k+1)^2 + (K^2+(k+1))
Ah, oops. I factored it incorrectly, myself. You should have $\displaystyle (k+1)^2\left(\frac{k^2}{4}+(k+1)\right)=(k+1)^2\le ft(\frac{k^2+4k+4}{4}\right)=(k+1)^2\frac{(k+2)^2} {4} $ This gives it to you.
thanks man!
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