The infinite sum is when the whole infinite geometric series is summed up. To calculate the partial sum of a geometric sequence, either add up the needed number of terms or use this formula. {eq}S_n = \frac{(a_1(1 - R^n)}{(1 - R)} {/eq} The sum of a series is denoted ...
The sum of an infinite geometric series is of the form: S=a11−r where a1 is the first term and r is the ratio whose absolute value is less than 1. We know that the second term is the first term multiplied by the ratio. In other words: a1⋅r=1a1=1r Thus, the sum is the...
(A) 1/2 (B)1 (C) 3/2 (D)2 (E)5/2 相关知识点: 试题来源: 解析选A 1/2 :此无限等比数列求和公式为S∞=a1/(1-q) ,a1是首项,q是公比 所以代入数值后得 S∞=(1/4)/(1-1/2)=1/2 即为此等比数列的总和. 故选A 1/2 【此题的英文翻译】无穷等比数列 1/4+1/8+1/16+1/32+...
Find the sum of the infinite geometric series.∑_(n=1)^∞(1/4)^n Write your answer as an integer or a fraction in simplest form. 相关知识点: 试题来源: 解析 n=1F(1/4)^n +[1/4+(1/4)^2+(1/4)^3+⋯] 3/4[1+1/4+1/(4^2)+1/(4^3)+⋯-J] 3/4*1/(1-1/4)...
If ∣r∣<1∣r∣<1, then the geometric series converges to a finite sum and we can calculate the sum of the infinite series; and If ∣r∣=1∣r∣=1, then the geometric series is periodic and its sum to infinite terms can't be determined. On the other hand, to calculate the partia...
The formula for the sum of an infinite geometric series follows:for |r|1,s=(|a_1)/(1-r)|What is the sum for the following infinite series?8+4+2+1+1/2+ OA:16Strike ResetOB(15)/2Stike ResetOCStrike ResetD8Strike Reset 相关知识点: 试题来源: 解析 8+4+2+1+1/2+⋯ [OMm...
What is the formula for the sum of infinite geometric series? Where a is the initial value and r is the common ratio: a * (1/(1 - r)) Note that this formula only applies if |r|<1! If this is not the case, then the series diverges. What is the formula of the sum of GP?
一道数列数学题,不懂啊Determine the sum of the infinite geometric series;800+300+225/2+...不懂 是算什麽的最大值啊?怎麽算?和 答案 求无穷等比数列的和这里a1=800,q=3/8,项数n为无穷大用等比数列求和公式Sn=a1(1-q^n)/(1-q) 代入整理得Sn=1280(1-n*3^n/8^n)当n趋于无穷大时,n*3^n/...
解析 The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term. Not a Geometric or Arithmetic Sequence The series given is not geometric. Therefore, the infinite sum cannot be calculated. No solution...
()A. (1+√5)/2B.2C. √5D.3E.4 答案 【解析】E相关推荐 1【题目】T he sum of an infinite geometric series is a positivenumber S, and the second term in the series is 1.What is the smallest possible value of S?()A. (1+√5)/2B.2C. √5D.3E.4 反馈 收藏 ...