Question

use mathematical induction to prove the statement is true for all positive integers n the integer n^3+2n is divisible by 3 for every positive integer n

Answer 1

ok, so to prove something using induction whats the first step you need to do?

Answer 2

theres two steps

Answer 3

i am honestly not sure..

Answer 4

ok, the first step is to prove that n(1) is true

Answer 5

i remember a bit of that it's called your "base" i think. but what do i prove this equation against without it being equal to something?

Answer 6

this is more of a theorem youre proving

Answer 7

1^3+2(1)=?. the problems i have done like this have another equation in the "?" area

Answer 8

so for the first step n(1) = (1)^3 +2(1)= 1+2 = 3, so 3is divisable by 3

Answer 9

oh i see! yes it is

Answer 10

perfect!

Answer 11

see, its not equal to a number, they want you to show that the equation is equal to a number divisable by 3

Answer 12

so now that you showed its divisable by 1, you need to show step 2 which is....?

Answer 13

another fabulous question... sorry i don't know

Answer 14

lol, well whats the question asking?

Answer 15

i need to prove the statement true for all positive integers, but i'm going to assume that I shouldn't prove individually each number that is not negative.

Answer 16

well, you are going to prove each number. youre just not going to enter 2, 3, 4, 5,......into the statement.....so now the question is, do you see a pattern?

Answer 17

n(2) is 12 and n(3) is 33 so i can tell that they all seem divisible by 3,

Answer 18

if we showed it is true for 1, and we need to prove its true for EVERY natural number what you need to do is plug in "n+1" in to the statement

Answer 19

that will give us every natural number!

Answer 20

would i plug that in where all the "n" is? for example: (n+1)^3+2(n+1)

Answer 21

EXACTLY!! preform the binomial expansion, combine like terms and thats pretty much it.
i gotta run to class now, good luck with any other problems!

Answer 22

thanks!