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Mrrafil [7]
3 years ago
15

Evaluate the series 9 + 3 + 1 +

Mathematics
1 answer:
ryzh [129]3 years ago
8 0

Answer:

9 + 3 + 1 + ......... = 13.5

Step-by-step explanation:

The series 9 + 3 + 1 +  is the sum of an infinite geometric sequence. The first term of the series is 9 while the common ratio is 1/3;

to obtain the common ratio we obtain the quotient of any two successive terms, 3/9 or 1/3.

The sum of an infinite geometric series with first term a and common ratio r is given by;

S_{n}=\frac{a}{1-r}

Plug in the values of a and r into the formula;

S_{n}=\frac{9}{1-\frac{1}{3} }\\\\\\S_{n}=\frac{27}{2}=13.5

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Answer:

1) 11\sqrt{3}

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3) 20\sqrt{3}  + 15\sqrt{2}

4) 53 + 12\sqrt{10}

5) -2

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Step-by-step explanation:

1) 2\sqrt{12} + 3\sqrt{48} - \sqrt{75}

=(2 × 2\sqrt{3} )+ (3 × 4\sqrt{3}) - 5\sqrt{3}

= 4\sqrt{3} + 12\sqrt{3} - 5\sqrt{3}

= 11\sqrt{3}

2) 4\sqrt{8} -2\sqrt{98} + \sqrt{128}

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= 2\sqrt{2}

3) 5\sqrt{12\\} - 3\sqrt{18} + 4 \sqrt{72}  +2\sqrt{75}

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Hope the working out is clear and will help you. :)

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2 years ago
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