Mathematical Induction -- Sigma Notation (1 Viewer)

[MuffinMan]

How do you do them? I don't get it
plz help me
thanks in advance

 

[Jago]

...give an example doofus.

 

[MuffinMan]

while u r at it can someone remind me how to do inequalities for induction also
did mine long time ago and i forgot thanks

 

[Estel]

or read your textbook...

 

[MuffinMan]

like in general what do u do

 

[Estel]

You get your statement and write it without the sigma.
Then you proceed as per usual.

 

[Jago]

we're not qualified teachers, most of us can't explain it properly in words - only do it by example...

 

[Slidey]

You are given an (in)equality.

Determine if it is true for n=1 or some easy to check number near the 'start'.
To do this, substitute n=1 into the LHS, then the RHS. If LHS=RHS, it works.

Now assume that the (in)equality is true for some number, k. Let n=k.

Now test whether or not it is true for n=k+1.
Substitute n=k+1 into the LHS, noting that you are ASSUMING the case n=k is true.
Substitute n=k+1 into the RHS. Manipulate the LHS (typically) until you get the result you're looking for: LHS=RHS.

Make a general statement. I usually write something like: By mathematical induction, since it is true for n=k, n=k+1 and n=1, it is true for all natural numbers.

 

[thunderdax]

Sigma just means the sum of every integer from the bottom number to the top number... kind of. its hard to explain.

 

[MuffinMan]

like for sigma not. of from 1 -> n (n^3) = [n^2 . (n+1)^2] / 4
Jones and couchman 3 unit book 1 Q6 (p296)

 

[MuffinMan]

when i write it out like a series i cant simplify LHS=RHS for n=k+1

 

[BlackJack]

Give an exmaple... you're in principle supposed to remove the extra k+1 term from the sum of k terms, then substitute your assumption... After that you may be able to rearrange some factors. It depends on the question.