Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Mathematical Induction

Prove by mathematical induction that

is divisible by 5.

What I've done so far:

For n = 1

(true that it is divisible by 5)
For n = k

(assumed to be true that it is divisible by 5)
For n = k + 1

This is where the problem lies. How can I show that

is divisible by 5?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] Mathematical Induction

hi

Try:

Bob

ps. I'm working on the trig question and center. I'll post if I get anywhere.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Mathematical Induction

Okay, thank you very much bob!

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

greg1313

Member

Registered: 2016-12-19

Posts: 20

Re: [ASK] Mathematical Induction

hi

Try:

Please do not use a period for attempted multiplication.  What you indicated to the right of the equals sign is unambiguously
equivalent to the use of decimal numbers for the bases as in "seven point seven raised to the k exponent minus two point two
raised to the k exponent equal to ..." and so on.

Please use multiplication dots as Monox D. I-Fly did instead.  Or, use an asterisk or bracketing such as parentheses.

Here are a couple of suggested fixes:

Notice in the "behind-the=scenes" text how the use of inserting the back slash tightens the asterisks between characters, while at the same time spreading
the other characters out for better readability.

Last edited by greg1313 (2019-12-09 04:23:59)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: [ASK] Mathematical Induction

hi greg1313

Good point, thanks.  I'll try not to make this error in future.

Also using math tags you can do this:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob