FP1 mathematical induction

So i started from sub n = 1 and it is = to 5, which is divisible by 5. Then i have done the assumption step. But i am stuck after that, with n = k+1 terms. Can someone help please?

Reply 1

Zacken

Show that

f(k+1) - f(k)

is also divisible by 5.

Reply 2

emilyp2206

Original post by Zacken

Show that

f(k+1) - f(k)

is also divisible by 5.

im struggling on this question too, cant seem to get a five out of it, any chance you can offer a few more hints

Reply 3

tiny hobbit

Original post by alesha98

So i started from sub n = 1 and it is = to 5, which is divisible by 5. Then i have done the assumption step. But i am stuck after that, with n = k+1 terms. Can someone help please?

Original post by emilyp2206

im struggling on this question too, cant seem to get a five out of it, any chance you can offer a few more hints

When you have powers of two different numbers, it is useful to do f(k+1) - 2 f(k) or f(k+1) - 3 f(k) which makes one of the terms vanish.

Because this one has 2k in the powers, try f(k+1) - 4f(k).

It's a nasty question.

Reply 4

emilyp2206

Original post by tiny hobbit

i think i may have gone the wrong way about it, ended with 3^2k+1 - 4(3^2k-1)
and then i ended up in circles
:frown:

Reply 5

tiny hobbit

Original post by emilyp2206

i think i may have gone the wrong way about it, ended with 3^2k+1 - 4(3^2k-1)
and then i ended up in circles
:frown:

Now take out a common factor of the lowest power of 3, i.e. 3^(2k-1)

Reply 6

emilyp2206

OHHH multiplying by 4 should mean algebraically you get x + 4x = 5x in the simplest terms right?

eDIT- this was a different way, or a way that not works at all

(edited 7 years ago)

Reply 7

emilyp2206

Original post by tiny hobbit

Now take out a common factor of the lowest power of 3, i.e. 3^(2k-1)

im grinning, it worked, im happy and thankful

Reply 8

CrazyFoxes

http://www.examsolutions.net/maths-revision/syllabuses/OCR/period-1/FP1/module.php

Go through the mathematical inductions if u havent.Explains every little thing,if its to a power what u do and if its not to a power what u do.