Estimate the error in approximating the sum of the alternating harmonic series n=the sum of the first nine terms. 相关知识点: 试题来源: 解析 The ninth partial sum is given by S_9=1-1/2+1/3=⋯+1/9=0.756 ... The first term omitted is -1/10. with magnitude 0.1. By Theorem 9.9...
Darboux Sums and the Sum of the Alternating Harmonic SeriesPrimary 40A05Secondary 97I30" Darboux Sums and the Sum of the Alternating Harmonic Series ." Mathematics Magazine , 91(2), p. 96doi:10.1080/0025570X.2017.1408380Sánchez, Francisco
You can calculate the sum of a finite alternating harmonic series easy enough: 테마복사 N = 1000; n = 1:N; s = sum((2*mod(n,2)-1)./n) gives 테마복사 s = 0.6926 댓글 수: 0 댓글을 달려면 로그인하십시오.이...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, harmonic...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, harmonic, alternatin...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of ...
It is clear that the alternating Harmonic series converges: ∑n=1∞(−1)n+1n=log2.∑n=1∞(−1)n+1n=log2. Thus, Sk=∑n=k∞(−1)n+knSk=∑n=k∞(−1)n+kn converges for each kk. For each kk, the sum could be expressed either as log2−αlog2−α or α...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, harmonic, alternating h...
Such a decomposition provides a proof without words that the series converges to the particular sum, and there are a variety of interesting diagrams in the literature showing series as area decompositions. Decomposing a region using a convergent series with negative summands (such as an alternating...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, harmonic, ...