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Chapter 12: Q. 14 (page 839)

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers.

1+111+121+13...1+1n=n+1

Short Answer

Expert verified

The statement is proved by mathematical induction.

Step by step solution

01

Step 1. Given Information

The given expression is1+111+121+13...1+1n=n+1

02

Step 2. Check for n=1.

First, we show that formula is true whenn=1. Because

1+11=1+1=2

03

Step 2. Check statement for some k

Next, we assume that formula holds for some k, and we determine whether the formula then holds for k+1.We assume that

role="math" localid="1646974240600" 1+111+121+13...1+1k=k+1

04

Step 4. show for k+1.

1+111+121+13...1+1k1+1k+1=k+11+1k+1=k+1k+1+1k+1=k+1+1

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Most popular questions from this chapter

In Problems 71-82, find the sum of each sequence.

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