Calculus

How many terms of the series the summation from n equals 1 to infinity of the quotient of negative 1 raised to the n plus 1 power and n do we need to add in order to find the sum with an absolute value of its error to be less than 0.05? (4 points)

A) 20
B) 15
C) 17
D) The series diverges so no sum is possible.

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  1. ever think of actually writing the math?
    sum(n=1..infinity) (-1)^(n+1)/n
    or even better,
    ∑(n=1..∞) (-1)^(n+1)/n
    You know that if S_n = ∑(-1)^n a_n then
    |S - Sn| < a_(n+1)
    so you just need n such that
    1/(n+1) < 1/20
    n+1 > 20
    n > 19
    Check:
    ∑k=1..n for n= 18,19,20 is
    0.6661398
    0.7187714
    0.6687714
    S∞ = log2 = 0.69315

    you can read online about the alternating harmonic series

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