Question

There is absolutely no empirical evidence for the divergence of the harmonic series even though the series diverges. The partial sums just grow too slowly. To show​ this, suppose you had started with s 1 equals 1 the day the universe was​ formed, 13 billion years​ ago, and added a new term every second. About how large would the partial sum s Subscript n be​ today, assuming a​ 365-day year?

Answer 1

The partial sum s Subscript n today would be
`S_(13 \ billon)= 39.2523`

Explanation:

From the question we are told that

n = 13 billion years

The partial sum is given as

`S_(n) = 1+ ln(n) * ln(10)`

Converting n to seconds

`n = (13 * 10^9) * (365 days / year) *(24 hr /day) * (3600/h) = 4.09968 *10^(16)`

The

`S_(13billion) = 1 + ln(4.0*10^(16)) ln(10)`

`S_(13 \ billon)= 39.2523`