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Evaluate the series 1 + 4 + 16 + 64 + 256 + 1024.

User Vimard
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1 Answer

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Answer:

Explanation:

This is a geometric sequence, where each term is obtained by multiplying the previous term by 4. The first term is 1, and the common ratio is 4. We can use the formula for the sum of a finite geometric series to find the sum of the first six terms:

S = a(1 - rⁿ) / (1 - r)

where:

a = first term = 1

r = common ratio = 4

n = number of terms = 6

Plugging in the values, we get:

S = 1(1 - 4⁶) / (1 - 4)

S = - 1(1 - 4096) / 3

S = - 4095 / 3

Therefore, the sum of the series 1 + 4 + 16 + 64 + 256 + 1024 is -4095/3, or approximately -1365.

User Vikash Kesarwani
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