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2016년 4월 7일 목요일

kenneth A.로스 (Ross) 해석학 솔루션 입니다 7장~36장 솔루션

kenneth A.로스 (Ross) 해석학 솔루션 입니다 7장~36장

HWP 파일로 되있구요. 7장 ~ 36장까지 있습니다. 미리보기 확인하시고 다운 바랍니다.

Exercises 1

1. Prove that for all natural numbers .
proof)
Let .
Since , is true.
Suppose that is true. i.e.

So, is true.
By mathematical Induction, is true for all natural numbers .

2. Prove for all natural numbers .
proof)
Let .
Since , is true.
Suppose that is true. i.e.

So, is true.
By mathematical Induction, is true for all natural numbers .

3. Prove for all natural numbers .
proof)
Let .
Since , is true.
Suppose that is true. i.e.

So, is true.
By mathematical Induction, is true for all natural numbers .

4. (a) Guess a formula for by evaluating the sum for and . [For , the sum is simply .]
sol.)

So, we guess .

(b) Prove your formula using mathematical induction.
proof)
Let .
Since , is true.
Suppose that is true. i.e.

So, is true.
By mathematical Induction, is true for all natural n

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