Prove

Prove that...(pic)

In today's age, one could simply add them all up. 0.307... < 0.375

Perhaps regroup? 1/2 - 1/12 - 1/30 - 1/56 - ... etc. Will those terms be turning positive any time? Can we just take enough terms to get less than (3/8 - 1/2010) and be done?

Let's see what you conclude?

I'm wondering if you professors with progressive thinking would take a chart as proof...
 

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Prove that...(pic)
The problem iinvolves a finite series. However, it is possible
to compare it to this infinite series:

ln(2) = 1 - 1/2 + 1/3 - 1/4 + ...
-1 + ln(2) = -1/2 + 1/3 - 1/4 + ...
1 - ln(2) = 1/2 - 1/3 + 1/4 - ... ~ 0.307

The finite series is greater than this, because it ends with the positive 1/2,010 term.

Even if you overcompensated and added 1/1,000 to 1 - ln(2) to more than make up
for the difference, it would be:
~0.307 + 0.001 ~ 0.308 < 0.375 = 3/8
 
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