1. ## Certain Question

2. Originally Posted by KatanaMaster95

Plug and chug, as they say...

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

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

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

You try some.

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

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

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

$(c)$ Clearly,

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

So, $S^2 = C.$

3. Originally Posted by Anonymous1
Complete detailed solution to routine question deleted
Do you get extra credit for this from the OP's school?

CB

4. I'm sorry, did I do something wrong here? I may have passed over this one in the MHF list of rules.