1+1/2+1/3+...+1/n = ln (n)+c, where c is Euler constant.

sn = 1+ 1/2+ 1/3+…+ 1/n & gt； ln( 1+ 1)+ln( 1+ 1/2)+ln( 1+ 1/3)+…+ln( 1+ 1/n)= ln[2 * 3/2 * 4/3 *……*(n+ 1)/n]

=ln(n+ 1)

Extended data:

Euler-Mas Ceroni constant

Euler-Mas Ceroni constant is a mathematical constant mainly used in number theory. Its definition is the limit of the difference between harmonic series and natural logarithm.

Leonhard euler, a Swiss mathematician, defined Euler's constant for the first time in the article arithmetic progression's Observation published in 1735. Euler used c as its symbol and calculated its first six decimal places.

In 176 1, he calculated the value to 16 digits after the decimal point. 1790, Italian mathematician Lorenzo Mascheroni introduced γ as the symbol of this constant and calculated it to 32 decimal places. But later calculations showed that he made a mistake in the 20th place.

Euler number is named after the world famous mathematician Euler; There is also a little-known name, Napier constant, to commemorate the introduction of logarithm by Scottish mathematician John Napier.

References:

Baidu Encyclopedia-Euler Constant