Solving Induction Problems: Making it Look Like You Want It To

[nastygoalie89]

Homework Statement

I understand the process of induction and how it works, but when it wittles down I have a hard time, as my teacher says "making the problem look like you want it to." It's just algebraic stuff showing P(k+1) is true

Homework Equations

1. (4 ^k+1-1) + 4^k+1 is equivalent to: 4(4^K+1-16) over 3

2. (1 over 2k+3) x (1 over 2k+4) is equivalent to: 1 over (2k+4)!

The Attempt at a Solution

This is after I have plugged in k+1 for n and simplified as best I could.

For 2. I work the factorial on the right side and have a (2k+2) x (2k+1) remaining after the 2k+3 and 2k+4 have canceled out.

 

[Mark44]

Homework Statement

I understand the process of induction and how it works, but when it wittles down I have a hard time, as my teacher says "making the problem look like you want it to." It's just algebraic stuff showing P(k+1) is true

Homework Equations

1. (4 ^k+1-1) + 4^k+1 is equivalent to: 4(4^K+1-16) over 3

2. (1 over 2k+3) x (1 over 2k+4) is equivalent to: 1 over (2k+4)!

The Attempt at a Solution

This is after I have plugged in k+1 for n and simplified as best I could.

For 2. I work the factorial on the right side and have a (2k+2) x (2k+1) remaining after the 2k+3 and 2k+4 have canceled out.

For each of these problems you need to do three things:

1. Establish that the statement is true for some starting point (typically n = 1 - the "base case").
2. Assume that the statement is true for n = k.
3. Show that if the statement is true for n = k, then the statement must also be true for n = k + 1.