sammietaygreen
  • sammietaygreen
Does the series converge or diverge? If it converges, what is the sum? infinity to n-1 -4(-1/2)^n-1
Mathematics
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SOLVED
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katieb
  • katieb
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sammietaygreen
  • sammietaygreen
sammietaygreen
  • sammietaygreen
I know it converges.
anonymous
  • anonymous
Do you know how to write the first four terms?

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More answers

sammietaygreen
  • sammietaygreen
No.. not sure
Vocaloid
  • Vocaloid
this is a geometric series with |r| < 1, so it converges you don't even have to write out the first terms if you don't want to
sammietaygreen
  • sammietaygreen
yes, but how do I calculate the answer?
Vocaloid
  • Vocaloid
Oh, right, it's asking for the sum, too the sum of a geometric sequence is S = a1/(1-r) where a1 is the first term and r is the common ratio
sammietaygreen
  • sammietaygreen
8/3?
sammietaygreen
  • sammietaygreen
I still don't completely understand. Sorry.
Vocaloid
  • Vocaloid
not quite, r = -1/2
Vocaloid
  • Vocaloid
a1 = -4(1/2)^0 = -4
sammietaygreen
  • sammietaygreen
Oh!! I think I get it now.
sammietaygreen
  • sammietaygreen
is it because it has 1/2 in the equation?
Vocaloid
  • Vocaloid
well, sort of the general form of a geometric sequence is a1(r)^(n-1), so, yes, r = -1/2

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