• Support PF! Buy your school textbooks, materials and every day products Here!

Induction help

  • #1

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) + 4k+1 is equivalent to: 4(4K+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 cancelled out.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
33,506
5,192

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) + 4k+1 is equivalent to: 4(4K+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 cancelled 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.
 

Related Threads on Induction help

  • Last Post
Replies
5
Views
973
  • Last Post
Replies
2
Views
743
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
8
Views
884
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
1K
Replies
4
Views
3K
Replies
4
Views
821
Top