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....
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...
The sum of an infinite geometric sequence is 12 and the first term is 3. What is the
When the sum of an infinite geometric series exists, we can calculate the sum. The formula for the sum of an infinite series is related to the formula for the sum of the first nn terms of a geometric series. Sn=a1(1−rn)1−rSn=1−ra1(1−rn)...
Answer to: Find the sum of the infinite geometric series. \sum_{n = 0}^{\infty}\left ( -\frac{1}{2} \right )^n By signing up, you'll get thousands...
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) 1/2 (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)...
Find the sum of the infinite geometric series1+3x+9x2+27x3+….. View Solution Sum of infinite terms of the series 1+47+972+1673+2574+……,is View Solution The sum of the infinite series(13)2+13(13)4+15(13)6+...is View Solution ...
Use this step-by-step Geometric Series Calculator, to compute the sum of an infinite geometric series providing the initial term a and the constant ratio r