Thread: Determining Formulas for Mathematical Induction

1. Determining Formulas for Mathematical Induction

I'm not sure how to approach these two problems, I've been trying for a couple hours and am getting nowhere. Could someone explain how I'm supposed to solve these?

For each of the following functions f with domain N determine a formula for f(n) and use mathematical induction to prove your conclusion.

1)f(1)=1/2, and for n>1 f(n)=(n-1)(f(n-1)-1/n+1
I've been trying to find an f(n-1) that will make this equality true, but I can't find anyway around the 0 multiplication in the first term, so I must be misunderstanding the problem.

2)f(1)=1 and for n>1 f(n)=(n+1)/3n*(f(n-1))

Any help understanding what this problem is asking for would be greatly appreciated!

2. Re: Determining Formulas for Mathematical Induction

Originally Posted by renolovexoxo
I'm not sure how to approach these two problems, I've been trying for a couple hours and am getting nowhere. Could someone explain how I'm supposed to solve these?

For each of the following functions f with domain N determine a formula for f(n) and use mathematical induction to prove your conclusion.

1)f(1)=1/2, and for n>1 f(n)=(n-1)(f(n-1)-1/n+1
I've been trying to find an f(n-1) that will make this equality true, but I can't find anyway around the 0 multiplication in the first term, so I must be misunderstanding the problem.

2)f(1)=1 and for n>1 f(n)=(n+1)/3n*(f(n-1))

Any help understanding what this problem is asking for would be greatly appreciated!
Please group your symbols properly in the first, it's unreadable as is. The second question is also ambiguous (though not as bad as the first).

3. Re: Determining Formulas for Mathematical Induction

1)f(1)=1/2, and for n>1 f(n)=((n-1)(f(n-1)) - (1/n+1)

2)f(1)=1 and for n>1 f(n)=((n+1)/3n) * ((n-1))

4. Re: Determining Formulas for Mathematical Induction

Have you tried calculating some values? For the first one f(1)= 1/2 so f(2)= ((2- 1)(1/2)- 1/(2+ 1)= 1/2- 1/3= 1/6.
f(3)= ((3-1)(1/6)- (1/4)= 1/3- 1/4= 1/12
f(4)= ((4- 1)(1/12)- (1/5)= 1/4- 1/5= 1/20.
Do you see the point now?
Do you see that (1/n)- (1/(n+1))= 1/[n(n+1)]

(I am assuming that your "(1/n+1)" is really "1/(n+1)"

5. Re: Determining Formulas for Mathematical Induction

Oh! I hadn't though of approaching it using those values. I'll see where I can get doing that. Thank you!