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MAVERICK [17]
3 years ago
10

What is the sum of series is numbers 64&66 ? Using the summation notation

Mathematics
1 answer:
iragen [17]3 years ago
4 0

Answer:

64. 6138

66. 8.078125

Step-by-step explanation:

Let's take it one number at a time.

For number 64:

6(2)^{1-1}=6

6(2)^{2-1}=12

6(2)^{3-1}=24

6(2)^{4-1}=48

6(2)^{5-1}=96

6(2)^{6-1}=192

6(2)^{7-1}=384

6(2)^{8-1}=768

6(2)^{9-1}=1536

6(2)^{10-1}=3072

Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072

Sum = 6138

For number 66:

12(-\frac{1}{2})^{0}=12

12(-\frac{1}{2})^{1}=-6

12(-\frac{1}{2})^{2}=3

12(-\frac{1}{2})^{3}=-1.5

12(-\frac{1}{2})^{4}=0.75

12(-\frac{1}{2})^{5}=-0.375

12(-\frac{1}{2})^{6}=0.1875

12(-\frac{1}{2})^{7}=-0.0078125

12(-\frac{1}{2})^{8}=0.046875

12(-\frac{1}{2})^{9}=-0.0234375

Sum = 12 + -6 + 3 + -1.5 + 0.75 + -0.375 + 0.1875 + -0.0078125 + 0.046875 + -0.0234375

or to make things simpler:

Sum = 12 - 6 + 3 - 1.5 + 0.75 - 0.375 + 0.1875 - 0.0078125 + 0.046875 - 0.0234375

Sum = 8.078125

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\Large\texttt{Answer\::}

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\Large\texttt{Calculations\::}

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