Mathematics Exam > Mathematics Questions > The series 13 + 23 + 33 + .... isa)divergentb...
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The series 13 + 23 + 33 + .... is
- a)divergent
- b)convergent
- c)bounded
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The series 13 + 23 + 33 + .... isa)divergentb)convergentc)boundedd)Non...
{Sn} is increasing sequence and unbounded from above.
∴ It is divergent sequence.
Hence, the series is divergent series.
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Community Answer
The series 13 + 23 + 33 + .... isa)divergentb)convergentc)boundedd)Non...
Series Analysis:
The given series is 13, 23, 33, ...
To determine whether the series is divergent, convergent, bounded, or none of these, we need to analyze the pattern and behavior of the terms.
Pattern Analysis:
Looking at the terms of the series, we can observe that each term is obtained by adding 10 to the previous term.
13 + 10 = 23
23 + 10 = 33
33 + 10 = 43
...
Therefore, we can represent the nth term of the series as:
Tn = 13 + (n-1) * 10
Convergence Analysis:
To determine if the series is convergent, we need to check if the terms approach a specific value as n approaches infinity.
In this case, as n increases, the terms of the series continue to increase without bound. The terms do not approach a specific value but instead grow infinitely larger.
Divergent Series:
A series is considered divergent if the terms do not approach a specific value and instead grow infinitely larger or oscillate between different values.
Based on the pattern and behavior of the terms in the given series, we can conclude that the series is divergent.
Therefore, the correct answer is option A) divergent.
The given series is 13, 23, 33, ...
To determine whether the series is divergent, convergent, bounded, or none of these, we need to analyze the pattern and behavior of the terms.
Pattern Analysis:
Looking at the terms of the series, we can observe that each term is obtained by adding 10 to the previous term.
13 + 10 = 23
23 + 10 = 33
33 + 10 = 43
...
Therefore, we can represent the nth term of the series as:
Tn = 13 + (n-1) * 10
Convergence Analysis:
To determine if the series is convergent, we need to check if the terms approach a specific value as n approaches infinity.
In this case, as n increases, the terms of the series continue to increase without bound. The terms do not approach a specific value but instead grow infinitely larger.
Divergent Series:
A series is considered divergent if the terms do not approach a specific value and instead grow infinitely larger or oscillate between different values.
Based on the pattern and behavior of the terms in the given series, we can conclude that the series is divergent.
Therefore, the correct answer is option A) divergent.
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