math induction questions (1 Viewer)

[.ben]

hi,
do you know when you're proving the LHS in step 1 in induction, do you substitute n=1 into the general nth term or do you take the first term? e.g. 1+27+125+...+(2n-1)^3=n^2(2n^2-1) is it:
LHS=1 (first term)

or

LHS=(2.1-1)^3
=(2-1)^3
=(1)^3
=1

-----------------------

thanks

 

[icycloud]

For n = 1,

LHS = (2n-1)^3
= (2[1]-1)^3
= 1

RHS = n^2(2n^2-1)
= 1^2(2[1]^2-1)
= 1 * 1
= 1

Thus, LHS = RHS, true for n = 1.

 

[acmilan]

It shouldnt matter, they should both be the same if n = 1 is the first term

 

[Riviet]

Make sure you read the question carefully. Alot of time you are not asked to prove for n=1, check the restriction of values that you are asked to prove in the question.

 

[.ben]

sometimes both steps aren't teh same? how come?

 

[acmilan]

If its a series, it should be.

But for examples like the one you posted in the other thread, ie. d/dx xⁿ = nx^n-1, you need to sub in n = 1 to both sides.

 

[.ben]

o alright, so it only works for series questions? ok cool thks.