What is the sum of the infinite geometric series? -3-3/2-3/4-3/8-3/16

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Question:

What is the sum of the infinite geometric series? -3-3/2-3/4-3/8-3/16

Answer:

Answer: -6.

Step-by-step explanation: Given geometric series is-

?f= 3%2C~ %5Cdfrac%7B3%7D%7B2%7D%2C%20~ %5Cdfrac%7B3%7D%7B4%7D%2C%20~ %5Cdfrac%7B3%7D%7B8%7D%2C~ %5Cdfrac%7B3%7D%7B16%7D%2C..

Here, the first term of the series, ?f=a%3D 3

and the common ratio, ?f=r%3D%5Cdfrac%7B1%7D%7B2%7D

Since it is an infinite series, so sum is given by

?f=S%3D%5Cdfrac%7Ba%7D%7B1 r%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20S%3D%5Cdfrac%7B 3%7D%7B1 %5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20S%3D%5Cdfrac%7B 6%7D%7B2 1%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20S%3D 6

Thus, the sum of the series is -6.

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