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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...

Question 1

the sequence was show below


tn = 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

tn - tn+1 = [ln(n+1) - ln(n)] - 1/(n+1)

as a difference of areas to show that tn - tn+1 > 0. Therefore, { tn } is a decreasing sequence.


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

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