Math Problem Statement

The sum of the first n terms of. geometric sequence is given by Sn= the summation of 2/3(7/8)^r from r=1 to n. Define the question. Find the first term of the sequence u1. Find S subscript infinity. Find the least value of n such that s subscript infinity - Sn <0.001.

Solution

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Math Problem Analysis

Mathematical Concepts

Geometric Sequences
Infinite Series
Summation

Formulas

Geometric sum formula: Sn = a(1 - r^n)/(1 - r)
Sum to infinity: S∞ = a / (1 - r)

Theorems

Convergence of geometric series when |r| < 1

Suitable Grade Level

Grades 10-12

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