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Svetach [21]
3 years ago
9

Calculate the sum of the infinite series

Mathematics
2 answers:
andriy [413]3 years ago
5 0
ANSWER

S_ \infty = \frac{40}{3}

EXPLANATION

The given series is

20-10+5-...


The first term of the series is,

a_1=20

The common ratio of this series is,

r = \frac{ - 10}{20}

This simplifies to,

r = - \frac{1}{2}

The sum to infinity of this sequence is given by the formula,

S_ \infty = \frac{a_1}{1-r}

We substitute the above values into the formula to obtain,

S_ \infty = \frac{20}{1- - \frac{1}{2} }

This simplifies to,

S_ \infty = \frac{20}{1 + \frac{1}{2} }

We simplify the denominator to get,

S_ \infty = \frac{20}{ \frac{3}{2} }

This will finally give us,

S_ \infty =20 \times \frac{2}{3}

S_ \infty = \frac{40}{3}

The correct answer is A.
kondor19780726 [428]3 years ago
4 0

Answer:

A. 40/3  is the correct choice


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