How to find the limit of a sum of a series? Im doing my homework on Infinite Series and I need help how to find the limits of the sums of the series. For example: So I know that a = 1/4 and r = 1/4 and since: The series converges. This was just an example. How do I...
If the nth partial sum of a series ∑limits ^(∞ )_(n=1)a_n is s_n= (n-1)(n+1), find a_n and ∑limits ^(∞ )_(n=1)a_n. 相关知识点: 试题来源: 解析For n=1, a_1=0 since s_1=0. For n>1.a_n=s_n-s_(n-1)= (n-1)(n+1)- ((n-1)-1)((n-1)...
Series which can be present as the partial sum such that which all term get cancel except it's first and the last term then it has finite sum this type of series is called telescoping series. Telescoping series is always convergent as it has a finite sum. ...
Find the partial sum {eq}S_5 {/eq} of the series {eq}\sum_{n=1}^\infty \frac{n}{2^n} {/eq} Determining The Partial Sum of a Series: Let {eq}{{a_n}} {/eq} be sequence of real numbers. The partial sum sequence is denoted by {eq}s_n {/eq} and defin...
Use the partial fraction command on your CAS to find a convenient expression for the partial sum, and then use this expression to find the sum of the series. Check your answer by using the CAS to sum the series directly.∑limits _(n=1)^(∞ ) (3n^2+3n+1)((n^2+n)^3)...
百度试题 结果1 题目In Exercise, find the partial sum.∑limits_(n=11)^(30)n-∑limits_(n=1)^(10)n 相关知识点: 试题来源: 解析 355
百度试题 结果1 题目【题目】Find the first four partial sums and the nthpartial sum of the sequence an.a_n=√n-√(n+1) 相关知识点: 试题来源: 解析 【解析】1-√2,1-√3,-1,1-√5;S_n=1- √3,-1,1-√5;S_n=1-√(n+) 1 ...
百度试题 结果1 题目In Exercise, find (a) the fourth partial sum and (b) the sum of the infinite series.∑limits_(j=1)^∞8(10^j) 相关知识点: 试题来源: 解析 (a) (1111)(1250) (b) 89
Find a formula for the nth partial sum of the series and use it to find the sum of the series if it converges. 18 / 1^2 . 2^2 + 30 / 2^2 . 3^2 + 42 / 3^2 . 4^2 + ... + 6(2n + 1) / n^2(n^2 + 1) + ....
【题目】Use a graphing utility to find the indicated partial sum s, and complete the table. T hen usea graphing utility to graph the first 1o termsof the sequence of partial sums. For each series, compare the rate at which the sequence ofpartial sums approaches the sum of the serie① ...