Find the sum of the geometric series by using a formula?

1-4+16-64+256-1024+4096?

Question

Find the sum of the geometric series by using a formula?

1-4+16-64+256-1024+4096?

tkhunny · Answer

Rewrite: $1 + 1\cdot (-4) + 1\cdot(-4)^{2} + 1\cdot(-4)^{3} + 1\cdot(-4)^{4} + 1\cdot(-4)^{5} + 1\cdot(-4)^{6}$

anonymous · Answer

Do you know the formula for the sum of a finite geometric series?

anonymous · Answer

Yes it's 

Sn=a1 { (1+1)^n  -1/1

anonymous · Answer

hmmm...may want to try that again, it looks a little off, unless I am misreading it.

tkhunny · Answer

I do, but I never use it.  I just make it up on the fly.  Let's see...$\dfrac{1 - 1\cdot(-4)^{7}}{1-(-4)}$

anonymous · Answer

$$Sn=a _{1} \left[ (1+1)^{n}-1 \right] / 1$$

anonymous · Answer

$$S _{n} = a _{1}\frac{ 1-r ^{n} }{ 1-r } $$

anonymous · Answer

Yes, yes, yes. sorry

anonymous · Answer

a1=1, n=7 and that's all we need.

anonymous · Answer

$$S _{7}=\frac{ 1-\left( -4 \right)7 }{ 1-(-4) }$$ which becomes $$\frac{ 16385 }{ 5 }=3277$$

anonymous · Answer

ok, I see

anonymous · Answer

Good, coz all I see are commands...stupid pc is not enabling math...lol

tkhunny · Answer

Just learn where the formula comes from.  FAR more useful than memorizing a formula!

anonymous · Answer

Agreed @tkhunny

anonymous · Answer

Thanks a lot guys!