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

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.)
S…(생략)