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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?

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okpalawalter8

Answer:

The partial sum s Subscript n today would be [tex]S_{13 \ billon}= 39.2523[/tex]

Step-by-step explanation:

From the question we are told that

           n = 13 billion years

The partial sum is given as

          [tex]S_{n} = 1+ ln(n) * ln(10)[/tex]

Converting n to seconds  

       [tex]n = (13 * 10^9) * (365 days / year) *(24 hr /day) * (3600/h) = 4.09968 *10^{16}[/tex]

The

       [tex]S_{13billion} = 1 + ln(4.0*10^{16}) ln(10)[/tex]

                      [tex]S_{13 \ billon}= 39.2523[/tex]