just plugging the various values for n, I get
sum(1..∞) = ln 2 = 0.69314718
so we want the sum to lie between 0.69304 and 0.69324
sum(1..9) = 0.7456
sum(1..99) = 0.6981
sum(1..999) = 0.6936
sum(1..9999) = 0.693197 <<*******
Given that the series the summation (from n = 1 to infinity) ((-1)^(n + 1))/n is convergent, find a value of n for which the nth partial sum is guaranteed to approximate the sum of the series with an error of less than 0.0001.
9
99
999
9999
1 answer