I made it into a Picture file, please help:

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- May 6th 2010, 10:15 AM #1

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- May 6th 2010, 11:08 AM #2
Plug and chug, as they say...

$\displaystyle (a)$ $\displaystyle S = \frac{n(n+1)}{2}$

$\displaystyle S(1) = \frac{1\cdot(1+1)}{2} = 1.$

$\displaystyle S(2) = \frac{2\cdot(2+1)}{2} = 1 + 2 = 3.$

You try some.

$\displaystyle (b)$ $\displaystyle C = \frac{n^2 (n+1)^2}{4}$

$\displaystyle C(1) = \frac{1^2 \cdot(1+1)^2}{4} = 1^3 = 1.$

$\displaystyle C(2) = \frac{2^2\cdot(2+1)^2}{4} = 1^3 + 2^3 = 9.$

$\displaystyle (c)$ Clearly,

$\displaystyle S^2 = (\frac{n(n+1)}{2})^2 = \frac{n^2(n+1)^2}{2^2} = C.$

So, $\displaystyle S^2 = C.$

- May 6th 2010, 10:50 PM #3

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- May 6th 2010, 11:10 PM #4