Question 462802: Notice that the sequence 1, ½, 1/3, ¼, ¼…., whose nth term is 1/n, is a decreasing sequence. Explain how to use this fact to determine if the following sequences are increasing or decreasing:
A. 2, 1 1/2, 1 1/3, 1 1/4, 1 1/5,…, 1 1/n
B. ½, 2/3, ¾, 4/5,…, n/n +1 (Hint: 2/3=1-1/3, ¾=1-1/4)
C. 1, ½^2, 1/3^2, ¼^2, 1/5^2,…,1/n^2
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! A) is decreasing because it is the same sequence, except each term is added with 1.
B) is increasing because each term is obtained by subtracting the terms of the original sequence from 1. It looks something like
1, 1-1/2, 1-1/3, 1-1/4, ...
C) is decreasing because it is the original sequence, except each term is squared. The function y = x^2 is monotonic for x > 0, so the original sequence decreasing implies that C) decreases as well.
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