相关知识点: 试题来源: 解析 e.g. The sequence 1,4,5,7,9,...,(1+(n-1)2),.. The sum of the first six terms would beS6=1+3+5+7+9+11=36Using the formula a=1 L=11 d=2S6=/2[1+11]=36Ta Da! 反馈 收藏
Answer to: 1) Determine the sum of the series. \sum_{n = 1}^{\infty} \left ( \frac{2^n + 9^n}{12^n} \right ) 2) Find the limit of the sequence a_n...
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Find a formula for the sum S_n of the first n terms of sequence. Then prove that your formula is true using mathematical induction.2, 6, 10, 14,…, (4n-2) 相关知识点: 试题来源: 解析 S_n=2n^2; Let P_n be the statement 2+6+10+14+⋯ +(4n-2)=2n^2. Because 2=2(1)...
The main purpose of this paper is to study two sum formulas of the sequences {a(n)}and {b(n)}. 利用数列a(n)和b(n)的性质,给出了a(n)和b(n)两个数列的求和公式。 3. Two sum formulas are given concerning these two numerical arrays. 给出了关于这两个数列的两个求和公式。 更多例...
Example 2: In an arithmetic sequence a, the sum of first n terms is Sn. I fS_3=6 , a_1=4 , find the common difference d. It is ( ).(A)1( B 5/3(C)-2(D)3 相关知识点: 试题来源: 解析Solution: (C) Method 1: By formula(3), we have d3 1 3 1 3 1 2 3-1 2 2...
The formula used to solve the sum of an arithmetic sequence is: n/22a + (n-1)d, where n = the number of terms to be added, a = the first term, and d = the constant value. What is an arithmetic sequence and give examples? Arithmetic sequences are series of numbers, like 2, 4...
a1. The nth triangular number is the sum of the numbers from 1 to n. The sequence goes 1, 3, 6,10, 15, 21, 28, ... At this point, they won't have a formula for the nth triangular number, just a procedure for finding it. 1. 第n个三角数字是数字的总和从1到n。 序列去1, ...
Formula for the sum of a finite Geometric Sequence: S_n=∑limits_n^(i=1)a_1r^(i-1)=a_1( (1-r^n)(1-r))Use summation notation to write the sum and then find the sum.1+10+100+...+100000 相关知识点: 试题来源: 解析 ∑limits _(i=1)^51(10)^(i-1), 111111 ...
An arithmetic sequence is a set of numbers in which the difference between consecutive terms is constant. The sum of an arithmetic sequence is calculated by using the formula given below: {eq}{S_n} = \dfrac{n}{2}\left[ {2{a_1} + \left( {n - 1} \right)d} \right]...