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- Thread starter Tyrion101
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Mentallic

Homework Helper

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Are you making an extra effort to think before you write when you encounter a negative sign?

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Harder (but ultimately better) solution: Develop the habit that every time you finish a problem (and also in the middle when you reach a stopping point), you check whether the answer you got makes sense. It's very unusual to have a problem where you can't check the answer somehow. You don't have to be 100% accurate, just good enough.

Here's an example: Someone asks you to find ##\sum_{n=1}^\infty {x^n \over n}## for ##\left|x\right| < 1##. You do a bunch of work and come up with ##\log(1-x)##. Instead of just typing it in right away, try plugging in a number for ##x## to see if the answer makes sense. As it turns out, if ##x = 1/2##, this answer does not make sense, because it is negative, whereas all the terms in the sequence were positive. So something went wrong, and you can now go through your work to locate it.

Another example: You have to find the point where ##\log(u+1) - u^2## is maximized. After a bunch of work, you get the answer 1/2. As a sanity check, the derivative should be zero there. It isn't, so something went wrong -- who knows exactly what, but something.

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