Find the sum of the first 20 terms of the geometric series -2 + 4 + -8 + ....

Question

anonymous · Answer

The first term of the GP is -2 and the ratio is -2.  What is the formula that links all of this.

anonymous · Answer

lol idk

anonymous · Answer

please dont comment if you arent gonna help. @callme911

australopithecus · Answer

sorry that would be
$$\sum_{n=1}^{20}(-1)^n 2^n$$

australopithecus · Answer

do you understand how I came to this solution?

australopithecus · Answer

or what to do next?

anonymous · Answer

whyd you delete it?

anonymous · Answer

Lol....u see it is G.P with r=-2

$$an=a*r ^{n-1}$$

anonymous · Answer

$$-2*-2^{19}$$

anonymous · Answer

$$=-2^{20}$$

anonymous · Answer

Hope that Helps

australopithecus · Answer

why did I delete what?

anonymous · Answer

no.. i do not

australopithecus · Answer

whenever you have a problem that  alternates from negative to positive you will have something like

(-1)^n

if it starts out as a positive then you will have

(-1)^(n+1)

australopithecus · Answer

remember  in the case of

(-1)^n

when n is even, (-1)^n equals a positive
when n is odd, (-1)^n equals a negative

australopithecus · Answer

so from the series I gave you

$$\sum_{n}^{\infty} (-1)^n (2)^n$$ 
= 
(-1)^(1)(2^1) + (-1)^2(2^2) + (-1)^(3)(2^3) + (-1)^(4)(2^4)...
-2 + 4 + -8 + 16...

australopithecus · Answer

do that 20 times and add them all and you have your answer

australopithecus · Answer

I think there may be a formula for these questions that makes it easier but I do not know it

anonymous · Answer

Lol.....@Australopithecus  no need to Do...that....we have Formulas

australopithecus · Answer

yeah I know yahoo!

australopithecus · Answer

I just dont know it lol

australopithecus · Answer

plus I wanted to demonstrate the operation

australopithecus · Answer

also at the bottom of that summation it should be n=1 not just n