Answer to Question #71702 in Discrete Mathematics for samir

Question

1. The number 3-540-97285-9 is obtained from a valid ISBN number by switching two
consecutive digits. Find the ISBN number. (You may write a code for this)
2. The number 0-31-030369-0 is obtained from a valid ISBN number by switching two
consecutive digits. Find the ISBN number. (The same code for question 14 should work for
this problem with a different input data too).
3. Prove by Principle of Mathematical Induction (PMI) that 3 | (4m3 + 5m) for every
nonnegative integer n
4. Prove by PMI that for every positive integer k,
1
2 *3
+
1
3* 4
+...........+
1
(k +1)*(k + 2)
=
k
2 * k + 4
5. Find a formula for 2+4+6+ ………+2m for every positive integer m and then verify your
formula by the PMI.
6. Let k ≥ 1 be an integer. Prove by PMI that 1+ k + k2 +..........+ kn =
kn+1 −1
k −1