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how many terms do you have to go for your approximation (your partial sum) to be within 0.0000001 from the convergent value of that series?

the answer to this question is 4, but i don't know how the book got 4. Probably a real easy question, but I am really confuse since there are no examples i can find, so can someone help? i really don't even know where to start, but i found this:

[tex] |s-s_n| \leq |s_n+1 - s_n| = b_n +1[/tex]

any help will be appreciated