For the series 3/2 + 3/4 + 3/8 + 3/16 + ...the sum will be calculated by the formula 
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<h3>What is number series?</h3>
When the numbers are arranged in a series with some logic then it is called as the number series.
here we have a series:
The sum of the series will be given as:
Hence for the series 3/2 + 3/4 + 3/8 + 3/16 + ...the sum will be calculated by the formula
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Answer:
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Step-by-step explanation:
1+1=2
Step-by-step explanation:
that is
sum(2^r) for r=1 to n, plus sum(1/2) for r=1 to n.
and that is
sum(2^r) + n/2 for r=1 to n.
2^r is a geometric sequence with 2 being the common ratio (every new term is created by multiplying the previous term by 2).
and since r is starting at 1, the first term a1 = 2.
the formula for the sum of a finite geometric sequence is
Sn = a1×(1 - r^n) / (1 - r)
with r being the common ratio .
so, in our case
Sn = 2×(1 - 2^n) / (1 - 2)
Sn = (2 - 2^(n+1)) / -1 = 2^(n+1) - 2
and so, in total we get
2^(n+1) - 2 + n/2 = 2^(n+1) + (n - 4)/2
Answer:
Although the cancellation law holds for addition, subtraction, multiplication and division of real and complex numbers (with the single exception of multiplication by zero and division of zero by another number), there are a number of algebraic structures where the cancellation law is not valid.
