- #1
Jamin2112
- 986
- 12
Here are some that I'm stuck on.
Pg. 56, #12
Prove by induction on n that, for all positive integers n, 3 divides 4^n + 5
Of course, the base case it is P(1) = (4^1 + 5) / 3 = 9/3 = 3...TRUE!
I just can't see the trick here. P(K+1)= (4^(K+1) + 5) / 3 = ((4)(4^K) + 5)/3= ... not getting anywhere, really.
Pg. 55, #17
For a positive integer n the number An is defined by
A1=1 [supposed to A with a subscript 1]
Ak+1 [supposed to A with a subscript k+1] = (6Ak+5)/(Ak+2)
Prove by induction on n that, for all positive integers (i) An>0 and (ii) An<5
I see by long division that we have
Ak+1=1-7/(Ak+2)... not sure if that helps. I know that Ak+1 will be zero with Ak=5...no sure if that helps though...
Pg. 56, #12
Prove by induction on n that, for all positive integers n, 3 divides 4^n + 5
Of course, the base case it is P(1) = (4^1 + 5) / 3 = 9/3 = 3...TRUE!
I just can't see the trick here. P(K+1)= (4^(K+1) + 5) / 3 = ((4)(4^K) + 5)/3= ... not getting anywhere, really.
Pg. 55, #17
For a positive integer n the number An is defined by
A1=1 [supposed to A with a subscript 1]
Ak+1 [supposed to A with a subscript k+1] = (6Ak+5)/(Ak+2)
Prove by induction on n that, for all positive integers (i) An>0 and (ii) An<5
I see by long division that we have
Ak+1=1-7/(Ak+2)... not sure if that helps. I know that Ak+1 will be zero with Ak=5...no sure if that helps though...