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16 Sep 2014, 00:50
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A sequence is defined as follows:
\(a_n = \frac{n}{n + 1}\)
If \(n\) is a positive integer, then how many of the first 100 terms of this sequence are less than 0.891?
A. 7
B. 8
C. 9
D. 10
E. 12
\(a_n = \frac{n}{n + 1}\)
If \(n\) is a positive integer, then how many of the first 100 terms of this sequence are less than 0.891?
A. 7
B. 8
C. 9
D. 10
E. 12
16 Sep 2014, 00:50
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Bookmarks
Official Solution:
A sequence is defined as follows:
\(a_n = \frac{n}{n + 1}\)
If \(n\) is a positive integer, then how many of the first 100 terms of this sequence are less than 0.891?
A. 7
B. 8
C. 9
D. 10
E. 12
Write out the first 10 terms of the sequence: \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{4}{5}\), \(\frac{5}{6}\), \(\frac{6}{7}\), \(\frac{7}{8}\), \(\frac{8}{9}\), \(\frac{9}{10}\), \(\frac{10}{11}\). Notice that any term in this sequence is larger than its predecessor. To determine how many terms are less than 0.891, we identify the first term that exceeds this value. The 9th term, \(\frac{9}{10}\), equals 0.9. Since the term before it, \(\frac{8}{9}\), is only 0.888..., only the first 8 terms of the sequence are less than 0.891.
Answer: B
A sequence is defined as follows:
\(a_n = \frac{n}{n + 1}\)
If \(n\) is a positive integer, then how many of the first 100 terms of this sequence are less than 0.891?
A. 7
B. 8
C. 9
D. 10
E. 12
Write out the first 10 terms of the sequence: \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{4}{5}\), \(\frac{5}{6}\), \(\frac{6}{7}\), \(\frac{7}{8}\), \(\frac{8}{9}\), \(\frac{9}{10}\), \(\frac{10}{11}\). Notice that any term in this sequence is larger than its predecessor. To determine how many terms are less than 0.891, we identify the first term that exceeds this value. The 9th term, \(\frac{9}{10}\), equals 0.9. Since the term before it, \(\frac{8}{9}\), is only 0.888..., only the first 8 terms of the sequence are less than 0.891.
Answer: B
05 Jul 2016, 00:17
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I make a calculation like that:
A=n/(n+1) ; A<0.891
1-A = 1/(n+1) ; 1-A > 0.109 . It means 1/ (n+1) > 0.891 or n+1 < 9.17
n<8.17 or the biggest n = 8
A=n/(n+1) ; A<0.891
1-A = 1/(n+1) ; 1-A > 0.109 . It means 1/ (n+1) > 0.891 or n+1 < 9.17
n<8.17 or the biggest n = 8
