Sarahisme Posted July 24, 2005 Share Posted July 24, 2005 can someone cleverer than me point out how this problem goes from the second last line to the last? Cheers Sarah Link to comment Share on other sites More sharing options...
Primarygun Posted July 24, 2005 Share Posted July 24, 2005 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 Link to comment Share on other sites More sharing options...
albertlee Posted July 24, 2005 Share Posted July 24, 2005 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. Link to comment Share on other sites More sharing options...
Sarahisme Posted July 24, 2005 Author Share Posted July 24, 2005 yep, ok , i see it now, thanks guys Link to comment Share on other sites More sharing options...
DQW Posted July 26, 2005 Share Posted July 26, 2005 [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] Link to comment Share on other sites More sharing options...
DQW Posted July 26, 2005 Share Posted July 26, 2005 More generally, notice that : [math]1-r^n = (1-r)(1+r+r^2+ \dots +r^{n-1})[/math] Link to comment Share on other sites More sharing options...
Primarygun Posted July 26, 2005 Share Posted July 26, 2005 oh ya, I forgot to put back the S. Link to comment Share on other sites More sharing options...
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