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...
Sum of Infinite Geometric Series: Formula & Evaluation When working with the sum of a geometric sequence, the series can be either infinite or finite. Sometimes, the problem asks for the sum of a number of terms. Other times, the problem asks for the sum of the infinite geometric series....
(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+...
()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 ...
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)...
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...
The sum of an infinite converges geometric sequence: $$\displaystyle S_{\infty } = \frac{a}{1-r} $$ Answer and Explanation: Given infinite geometric series: $$\displaystyle \sum_{n = 0}^{\infty}\left ( -\frac{1}{2} \right )^n = 1-\frac{1}{...
The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is2719. Then, the common ratio of this series is View Solution Free Ncert Solutions English Medium NCERT Solutions NCERT Solutions for Class 12 English Medium ...
Infinite Geometric Progression Given a geometric progression with infinite terms, with the first term asaand common ratior, The sum of the infinite terms is given as sum=a1−r|r|<1 Answer and Explanation:1 Given the geometric series as ...
Geometric Series - Sum to infinity IFYMaths GeometricSeriesSumtoInfinity Geometricseries–SumtoInfinitySupposewehavea2metrelengthofstring...whichwecutinhalf 1m1m Weleaveonehalfaloneandcutthe2ndinhalfagain 1m 12 m 14 12 m 14 ...andagaincutthelastpieceinhalf 1m 12 m m m Geometricseries–SumtoInf...