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Chapter 12: Q 27. (page 830)

In Problem, prove each statement.

1+an鈮�1+nafora>0

Short Answer

Expert verified

The given statement is shown.

Step by step solution

01

Step 1. Given information

1+an鈮�1+na

02

Step 2. Prove the given statement.

Put n=1in (1+a)n鈮�1+nato check if the statement is true for n=1.

width="121">(1+a)1鈮�1+(1)a1+a鈮�1+a

Thus, the statement is true for n=1

Assume that the statement is true for width="37">n=k

Thus, (1+a)k鈮�1+ka.

Find whether (1+a)k+1鈮�1+(k+1)a

(1+a)k+1=(1+a)k路(1+a)鈮�(1+ka)(1+a)鈮�1+ka2+a+ka鈮�(1+k)a+1+ka2鈮�(1+k)a+1

Thus, the statement is true fork+1

Since both the conditions of the Principle of Mathematical Induction are satisfied, the statement

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