can someone cleverer than me point out how this problem goes from the second last line to the last?

 

Cheers

 

Sarah

I haven't learnt Sigma yet, so I skip it here.

Let [Math] S=1+r+r^2+r^3+.....[/Math]

then [Math]rS=r+r^2+r^3+r^4+.....[/Math]

That's some problems. Oh, I think there should be a range for r considering what in your photo is.

[Math]rS-S=S(r-1)=-1/ (r-1)[/Math]

where I assume [Math]|r|<1[/Math]

I hope this can help you

I haven't learned those weird notations.

 

BUTBUTBUT, the formula is more or less called "Geometric Progression"

 

Google for that word, and you will help yourself out.

yep, ok , i see it now, thanks guys

[Math]rS-S=S(r-1)=-1/ (r-1)[/Math]

That is incorrect...or so it looks to me. I think you meant :

[Math]rS-S=S(r-1)=-1[/Math]

[math]\implies S = 1/(1-r) [/math]

More generally, notice that :

 

[math]1-r^n = (1-r)(1+r+r^2+ \dots +r^{n-1})[/math]

oh ya, I forgot to put back the S.