Question

Test
the
convergence
1/4.7.10 + 4/7.10.13/ .......​

Answer 1

Step-by-step explanation:

Step by step solution has been annexed.

Answer 2

Answer:

 The convergence of the sequence is found to be $\frac{4}{7}$

Step-by-step explanation:

As the nth term $T_{n}$=$\frac{1}{(3n-2)(3n+1)(3n+4)}$

We get a partial fraction via,

$T_{n}$=$\frac{1}{6} [\frac{1}{(3n-2)(3n+1)} -\frac{1}{(3n+1)(3n+4)} ]$

$T_{1}=\frac{1}{6}[\frac{1}{1.4}-\frac{1}{4.7} ]$

$T_{2}=\frac{1}{6}[\frac{1}{4.7}-\frac{1}{7.1} ]$

Then, Sn=∑Tn=$\frac{1}{6} [\frac{1}{1.4} -\frac{1}{(3n+1)(3n+4)} ]$

=$\frac{1}{24}-\frac{1}{6(3n+1)(3n+4)}$

As n⇒∞

$S_{n}=\frac{1}{24}-0\\=\frac{1}{24}$

As a conclusion, the sequence's 100th term is equal to ( $\frac{4}{7}$ ) 0f 99 times the first term, or 1/4.7.10. The convergence of the series is matched by the simplification of this to  $\frac{4}{7}$ . The sequence conforms to $\frac{4}{7}$ as a result.​

To learn more about partial fractions, visit,

https://brainly.in/question/51353920

To learn more about the sequence, visit,

https://brainly.com/question/21961097

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