Find the sum of the convergent series 4-2+1-1/2

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SUMMARY

The convergent series 4 - 2 + 1 - 1/2 can be expressed as a geometric series with the first term 4 and a common ratio of -1/2. The sum of this series can be calculated using the formula for the sum of a geometric series, S = a / (1 - r), where a is the first term and r is the common ratio. Substituting the values, the sum is 4 / (1 - (-1/2)) = 4 / (3/2) = 8/3. This confirms that the series converges to 8/3.

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find the sum of the convergent series 4-2+1-1/2 ...

Homework Statement



find the sum of the convergent series . 4-2+1-1/2...

Homework Equations



sum of r^n |r|< 1 --> 1/(1-r)= sum

The Attempt at a Solution


4(1-1/2+1/4-1/8...)
I can see a pattern here where the denominator is going 2,4,8 so its like 1*2, 2*2, 2*2*2 but the 1 and + and the - throws me off...can someoen help me?
 
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If this in fact is a geometric series, what would the common ratio be?
 


Hint: incorporate [itex](-1)^n[/itex] to solve your sign problem.
 

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