This problem is from Apostol's Caclulus book vol 1 page 35 or 36 #2(adsbygoogle = window.adsbygoogle || []).push({});

Show that

1 - 4 = -(1 + 2)

1 - 4 + 9 = 1 + 2 + 3

1 - 4 + 9 - 16 = -(1 + 2 + 3 + 4)

is true by mathematical in duction

I get to this step but have problem figuring out how to finish it off

-1^(n+1) * n^2 = -1^(n+1) * (n(n+1)/2)

I then do the plugging in bit and end up with

-1^(n+1) * (n(n+1)/2) + (-1^(n+2) * (n+1)^2) << the next term (n+1)

I have tried to work this out a few times but I cant seem to get a stable answer, any helps? Maybe i've forgotten some simple algebra tricks. The answer I think should look like

-1^(n+2) * ((n+1)(n+2)/2)

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# Mathematical Induction

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