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romanna [79]
3 years ago
10

The series 2/3+3/4+4/5 is divergent T or F

Mathematics
1 answer:
12345 [234]3 years ago
7 0

True, the series is indeed divergent.

The <em>n</em>-th term is given by

(<em>n</em> + 1) / (<em>n</em> + 2)

starting with <em>n</em> = 1, so that

(<em>n</em> + 1) / (<em>n</em> + 2) = (<em>n</em> + 2) / (<em>n</em> + 2) - 1 / (<em>n</em> + 2) = 1 - 1 / (<em>n</em> + 2)

and as <em>n</em> grows to infinity, the rational term vanishes, the summand converges to 1, and the sum behaves like ∑ 1, which diverges.

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