Statistics, Data Analysis and Probability for Grade 12, Problem ID: 7941
The interesting series shown is divergent, even though the terms get progressively smaller. The value of H(N) increases as N increases, and the infinite sum is said to have "an infinite" value. But just how big is that?
The ln( ) function is the natural logarithm and ln(10,000) = 9.2
Let's make N pretty large,
say one hundred thousand million billion
(100 x 1000 x 1,000,000 x 1,000,000,000 = 1020).
For a quick estimate, ignore Euler's constant (0.577215...) and pretend ln(10,000) = 10.
Without using a calculator, how big is H(N)?
by Leslie Green
greater than 10,000 but less than 1 milliongreater than 1 million but less than 1 billionless than 100 but greater than 10greater than 100 but less than 10,000