| Let P(n) be the claim: | n | 2j-1 | = |
2n - 1 | for all integers n 1. |
| S | |||||
| j = 1 | |||||
2c)
| Let P(n) be the claim: | n | 2j-1 | = |
2n - 1 | for all integers n1. |
| S | |||||
| j = 1 | |||||
| P(1) is the statement: | 1 | 2j-1 | = |
21 - 1. |
| S | ||||
| j = 1 | ||||
| P(k) is the statement: | k | 2j-1 | = |
2k - 1 |
| S | ||||
| j = 1 | ||||
| P(k+1) is the statement: | k + 1 | 2j-1 | = |
2k+1 - 1. |
| S | ||||
| j = 1 |
For a proof by induction, you first need to check that the statement P(1) is true. Then assume that P(k) is true and use this to show that P(k + 1) is true.