Write the sum using summation notation and then find the sum: 12, -4, 4/3, -4/9, ...

Question

adamk · Answer

So I've got $$\sum_{n = 1}^{\infty} 12(\frac{ -1 }{ 3 })^{n-1}$$

and the equation for a sum of an infinite series is A$$S _{\infty} = \frac{ A _{1} }{ r - 1 }$$ which I have to equal 9. Is that right?

sshayer · Answer

$$S _{\infty}=\frac{ a }{ 1-r }=\frac{ 12 }{ 1-(\frac{ -1 }{ 3 } )}=12 \times \frac{ 3 }{ 4 }=9$$

adamk · Answer

@sshayer So I am correct?

mathmale · Answer

Yes, you are to find the sum of an infinite geometric series.  Thanks for sharing your work.  Looks good!

sshayer · Answer

remember,in the denominator 1-r

mathmale · Answer

You've done fine.  But for communication's sake, identify your "first term:"  a = 12, and your "common ratio:"  r =-1/3.

adamk · Answer

Right

adamk · Answer

Yeah I meant to say 1-r.