| Let P(n) be the claim: | n | (2i - 1) | = |
n2 | for all integers n 1. |
| S | |||||
| i = 1 | |||||
2a)
| Let P(n) be the claim: | n | (2i - 1) | = |
n2 | for all integers n1. |
| S | |||||
| i = 1 | |||||
| P(1) is the statement: | 1 | (2i - 1) | = |
12. |
| S | ||||
| i = 1 | ||||
| P(k) is the statement: | k | (2i - 1) | = |
k2. |
| S | ||||
| i = 1 | ||||
| P(k+1) is the statement: | k + 1 | (2i - 1) | = |
(k + 1)2. |
| S | ||||
| i = 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.