Question 1

the sequence was show below

t_{n }= 1 + (1/2) + (1/3) + ... + (1/n) - ln(n)

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

(b) Interpret

t_{n }- t_{n+1 }= [ln(n+1) - ln(n)] - 1/(n+1)

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.

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