Question

Prove by mathematical Inducttion:
\( 10^{(n+1)} + 3.4^{(n-1)} +5 \) is divisible by 9

Answer 1

10^{(n + 1)}

That'd work :)

Answer 2

okkkk thanks u r awesosme parth

Answer 3

Let's start with 1.

\( \color{Black}{\Rightarrow 10^{2} + 3.4^{0} + 5 }\)

\( \color{Black}{\Rightarrow 100 + 1 + 5 }\)

\( \color{Black}{\Rightarrow 106}\)

Answer 4

Ya its not divisible by 9 so i guesss its not true

Answer 5

Never heard that 106 was divisible by 9.

Answer 6

Pretty sure 106 is not divisible by nine.

Answer 7

The way the question is phrased seems like these statemnets must be true but who knows

Answer 8

The question should have said - "Disprove by Mathematical Induction". Heh!

Answer 9

curious, what book are you using for these induction problems?

Answer 10

It says use the PMI to prove the following for all natural numbers

Answer 11

lol, 1 is also a natural number :P

Answer 12

A transition to advanced mathematics By douglas smith, Maurice eggen and Richard St andre

Answer 13

'advanced mathematics' is an overstatement.

Answer 14

maybe its \( 10^{n+1}+3 * 4^{n-1}+5 \) ????

Answer 15

YAAAAAAAAAAAAAAAAAAAA

Answer 16

I knew that the statement had to be true. ALRIGHTY THANKS

Answer 17

I am trying to solve it but i cant obviously

Answer 18

like how wld u prove its true for (n+1)?

Answer 19

can you show it is true for n=0 (that is the first step, prove true for the "base case")

Answer 20

umm well its all natural numbers so it n=1
10^2+3*4^0 +5 = 108
and 9 divides 108

Answer 21

ok, now assume it is true for all cases up to n
is it true for n+1?

replace n with n+1 in the equation, what do you get?

Answer 22

\( 10^ {(n+2)} + 3*4^n +5 \)

Answer 23

Like i am not sure how I am suppossed to show that this is divisible by 9

Answer 24

right now I am waiting for an idea to show up.

Answer 25

hahahahahahahah

Answer 26

10^n = 1 mod 9

Answer 27

I have learnt modulus but not in this course yet. like that is next chapter but i guess we can use ittttttttttt

Answer 28

exp that is helpful

this may not be the fastest way, but we could group like this
10*10^(n+1) + 4*3*4^(n-1) +5
6*10^(n+1) + 4*10^(n+1) + 4*3*4^(n-1)+ 4*5 -15

Answer 29

that becomes
6*10^(n+1) +4( stuff div by 9) -15
now we must show
6*10^(n+1)-15 is div by 9

Answer 30

well, the right thing to do is do assume it to be true up to n ... rigorously and prove it or n+1

Answer 31

man ... i'm not comfortable with group theory

Answer 32

ohhhhh i found a similar method

Answer 33

so we have the same sequence