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2. Adapt the formula 1 +2+3 + ... + (n – 1) + n = "x(n+1 to find S = 4 + 5 + 6 + ... + n+ (n+ 1). S=4+5+6+ ... +n+ (n + 1) =. +4 +5+6+...+n+ (n+ 1)-

2. Adapt the formula 1 +2+3 + ... + (n – 1) + n = "x(n+1 to find S = 4 + 5 + 6 + ... + n+ (n+ 1). S=4+5+6+ ... +n+ (n + 1) =. +4 +5+6+...+n+ (n+ 1)-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**1. Understanding Patterns in Sequences** Use the strategy of looking for a pattern to find the nth term of the sum O = 1 + 7 + 13 + 19 + … + t, where t is the nth term. Complete the following table: | | 1 | 2 | 3 | … | n-2 | n-1 | n | n+1 | |---|---|---|---|---|-----|-----|---|-----| | | | | | | | | | | **2. Adapting Formulas** Adapt the formula 1 + 2 + 3 + … + (n-1) + n = \( \frac{n \times (n + 1)}{2} \) to find S = 4 + 5 + 6 + … + n + (n+1). S = 4 + 5 + 6 + … + n + (n+1) = _____ + _____ + _____ + 4 + 5 + 6 + … + n + (n+1) - _____ The given sequence represents an arithmetic sequence where each term increases by a constant difference. The table and formulas are designed to help understand and apply pattern recognition in sequences and to adapt known formulas for summing series.
Transcribed Image Text:**1. Understanding Patterns in Sequences** Use the strategy of looking for a pattern to find the nth term of the sum O = 1 + 7 + 13 + 19 + … + t, where t is the nth term. Complete the following table: | | 1 | 2 | 3 | … | n-2 | n-1 | n | n+1 | |---|---|---|---|---|-----|-----|---|-----| | | | | | | | | | | **2. Adapting Formulas** Adapt the formula 1 + 2 + 3 + … + (n-1) + n = \( \frac{n \times (n + 1)}{2} \) to find S = 4 + 5 + 6 + … + n + (n+1). S = 4 + 5 + 6 + … + n + (n+1) = _____ + _____ + _____ + 4 + 5 + 6 + … + n + (n+1) - _____ The given sequence represents an arithmetic sequence where each term increases by a constant difference. The table and formulas are designed to help understand and apply pattern recognition in sequences and to adapt known formulas for summing series.
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