Proof Without Words: Partial Sums of an Arithmetic SequenceA visual proof that a partial sum of an arithmetic sequence equals the number of terms times the average of the first and last term.doi:10.4169/college.math.j.43.4.321Anthony J. Crachiola...
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We prove that the log-convexity of the partial sum for a log-convex sequence is preserved under a mild condition. As applications, we mainly discuss the log-convexity of the partial sums for many famous combi- natorial sequences.FENG-ZHEN ZHAO...
Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why....
Node1addsthesepartialsumstoget the finalsum. 节点1对这些部分和进行求和,从而得出最终的总和。 www.ibm.com 7. Nownode1hastwopartialsums. 现在节点1有两个部分和了。 www.ibm.com 8. Astronglawof largenumberofpartialsumsforpositivelyassociatedsequences ...
The partial sum of the infinite series can be found up to a certain number of terms. If the series is converging, then the limiting sum also will be finite. A series is formed by the sum of all the terms of the sequence. Answer and Explanation:1 ...
The sum of partial sums was extensively applied to mathematics and economics,such as random walk.In this paper,the weak law of large numbers for sum of partial sums of pairwise NQD sequences is discussed.Some results in the literature are improved and extended from the weak law of large nu...
Given a series {eq}\sum_{n = 1}^{\infty} a_n {/eq} its partial sums {eq}S_k {/eq} are given by: {eq}S_k=\sum_{n = 1}^{k} a_n \text{ for }k\ge 1. {/eq} In the event that the sequence of partial sums {eq}\{S_k\}_{k=1...
You are given a sequence of n numbers a0,..., an-1. A cyclic shift by k positions (0<=k<=n-1) results in the following sequence: akak+1,..., an-1, a0, a1,..., ak-1. How many of the n cyclic shifts satisfy the condition that the sum of the fi rst i numbers is grea...
摘要: Applying the weak law of large numbers of partial sums in NA sequences and moment inequality for maximum,the author obtains the weak law of large numbers for random sums of partial sums in NA sequences,which corresponds to the result in independent and identically distribution....