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If one simply uses some common sense when trying to solve this problem, this is a relatively easy problem to solve. First, you can find out that a = b = c by setting the three sums equal to each other. Once you find that out, you can convert any of these equations to 2a = a^3. The rest is also easy.
I don't like the part of the solution where you just say that 49 is kinda like infinity. Ok, the limit is eventually 2,7. But what values does it have for lower n? 1? 10? You must show that you are taking a safe upper bound for smaller values of n.
I think the first four are correct, but odd and even are defined for negative integers too so the so they either doesn't exist or approach negative infinity
@@harris5140 i meant to say that this question is stupid because just by looking at the thumbnail i was able to say that the left side is greater... But than again, in order to solve a mathematical question we need to provide a proof and that one is not that intuitive so the video is not useless, even tho everyone knows the answer to begin with. And Im not sure what x you are talking about as both of them are final numbers.
Alternatively, we use that (1+x)^n = 1 + nx + stuff To state that 1.005^200 = (1+0.005)^200 = 1 + 200*0.005 + stuff= 2+stuff Where stuff is positive, done :)
Yes, a much more elegant approach. "stuff" is the binomial expansion. Strictly speaking, though, would have to also demonstrate by formula that all of the binomial expansion coefficients are positive to get full score on an Olympiad.
