Use the following steps to show that the sequence

has a limit. (The value of the limit is denoted by γ and is called Euler’s constant.)

(a) Draw a picture like Figure 6 with f(x) = 1/x and interpret t_n as an area [or use (5)] to show that t_n > 0 for all n.

(b) Interpret

as a difference of areas to show that t_n – t_n+1 > 0. Therefore {t_n} is a decreasing sequence.

(c) Use the Monotonic Sequence Theorem to show that {t_n} is convergent.

Transcribed Image Text:

Inn I, = 1+ -/-