Harder MX1 (2 Viewers)

[J-Wang]

I have just proven that
The question then asks me to prove by induction that
Can someone please show me how to do this? I keep getting to a certain point and not knowing where to go from there.

Thanks in advance

 

[Alkenes]

have you done all 4u topics?

 

[J-Wang]

have you done all 4u topics?

We have like 3 more lessons to finish off mechanics and then yes

 

[J-Wang]

anyone know how?

 

[Riproot]

 

[J-Wang]

View attachment 25673

do u have access to a computer? then it will come up.

 

[seanieg89]

Will scan and upload a solution in a sec.

 

[J-Wang]

it says that i have proven that {[sin(3x)/2]-[sinx/2]}/2sinx/2 = cosx

i then have to prove by induction that cosx+cos2x+cos3x+...cosnx={[sin(2n+1)/2]x/2sinx/2 - 1/2
have any ideas?

 

[Riproot]

Ohhhh… I'll grab some a pen and paper and brb.

 

[seanieg89]

 

[seanieg89]

Apologies for the handwriting...

 

[J-Wang]

View attachment 25674

i follow ur solution, and it is correct, but i usually do it by assuming true for n=k and then proving true for n=k+1. if u apply ur solution to that scenario, it doesnt work. why is that?

 

[seanieg89]

It will work just the same, the expressions involved will just be marginally messier. You could literally copy the same proof and replace every instance of 'k' with 'k+1'.

 

[seanieg89]

Actually, I did that work in a bit of a rush and made a minor mistake in my layout. We are assuming that the identity holds for n-1, and then proving that it holds for n. We are NOT assuming that it holds for n=k-1 and proving that it holds for n=k.

 

[2ndt0m3h]

how did you prove the first result lol we haven't taken harder 3 unit and it looks so easy yet im not getting the answer.

 

[Carrotsticks]

View attachment 25674

I had a rather different proof in mind involving a Telescoping Sum because we're finding a Trigonometric Sum with the 'angles' (is that what you call it?) in A.P.

EDIT: Never mind I just saw they asked us to prove it via Induction.

 

[Carrotsticks]

btw I like your sigmas.

 

[seanieg89]

btw I like your sigmas.

Haha cheers, I know you have high standards in that regard. Yeah the series is just the real part of a complex geometric series, so it is very quick to evaluate without induction.

 

[Fus Ro Dah]

I had a rather different proof in mind involving a Telescoping Sum because we're finding a Trigonometric Sum with the 'angles' (is that what you call it?) in A.P.

EDIT: Never mind I just saw they asked us to prove it via Induction.

Using the Sums/Products and Products/Sums expression I presume?

 

[Carrotsticks]

Using the Sums/Products and Products/Sums expression I presume?

Yep!