Chapter 8: Q21RE (page 498)
If a finite number of terms are added to a convergent series, then the new series is still convergent.
The statement is true.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent?
\(\sum\limits_{n = 1}^\infty {\frac{1}{{\ln (n + 1)}}} \)
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent?
Find the value of \(c\) if \(\sum\limits_{n = 2}^\infty {{{(1 + c)}^{ - n}} = 2} \)
\(\sum\limits_{n = 1}^\infty {\frac{{1 + {2^n}}}{{{3^n}}}} \) find whether it is convergent or divergent and find its sum if it is convergent.
Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
\(\sum\limits_{n = 1}^\infty {\frac{{{{\left( {{\rm{ - }}1} \right)}^n}}}{{n{5^n}}}} \) \(\left( {\left| {error} \right| < 0.0001} \right)\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
