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irga5000 [103]
2 years ago
9

Find S11 for 1 + 2 + 4 + 8 + …

Mathematics
1 answer:
NemiM [27]2 years ago
5 0

Answer:

2,047

Step-by-step explanation:

Given:

1+2+4+8+...

Find:

S_{11}

You are given the geometric sequence. From the given sum, you can see that

b_1=1\\ \\b_2=2=1\cdot 2=b_1\cdot 2\\ \\b_3=4=2\cdot 2=b_2\cdot 2\\ \\b_4=8=4\cdot 2=b_3\cdot 2\\ \\....\\ \\r=2

To find the sum S_{11}, use formula

S_n=\dfrac{b_1(1-r^n)}{1-r}

Hence,

S_{11}=\dfrac{1\cdot (1-2^{11})}{1-2}=\dfrac{1-2,048}{-1}=2,047

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