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The sum of the series (1/2) + (1/3) + (1/6) + .... upto 9 terms is
- a)(-5/6)
- b)-(1/2)
- c)1
- d)-(3/2)
Correct answer is option 'D'. Can you explain this answer?
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The sum of the series (1/2) + (1/3) + (1/6) + .... upto 9 terms isa)(-...
Given series is (1/2) (1/3) (1/6) .... upto 9 terms.
To find the sum of the series, we can use the formula for the sum of the first n terms of a geometric progression:
S = a(1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this series, the first term is 1/2 and the common ratio is 1/2. So, we have:
a = 1/2
r = 1/2
n = 9
Substituting these values in the formula, we get:
S = (1/2)(1 - (1/2)^9) / (1 - 1/2)
S = (1/2)(1 - 1/512) / (1/2)
S = (1 - 1/512)
S = 511/512
Therefore, the sum of the series is 511/512.
Now, we need to simplify this fraction to check which option is correct.
511/512 can be written as (512 - 1)/512.
So, (512 - 1)/512 = 1 - 1/512.
Comparing this with the given options, we see that option D is the correct answer, which is -(3/2).
To find the sum of the series, we can use the formula for the sum of the first n terms of a geometric progression:
S = a(1 - r^n) / (1 - r)
where a is the first term, r is the common ratio, and n is the number of terms.
In this series, the first term is 1/2 and the common ratio is 1/2. So, we have:
a = 1/2
r = 1/2
n = 9
Substituting these values in the formula, we get:
S = (1/2)(1 - (1/2)^9) / (1 - 1/2)
S = (1/2)(1 - 1/512) / (1/2)
S = (1 - 1/512)
S = 511/512
Therefore, the sum of the series is 511/512.
Now, we need to simplify this fraction to check which option is correct.
511/512 can be written as (512 - 1)/512.
So, (512 - 1)/512 = 1 - 1/512.
Comparing this with the given options, we see that option D is the correct answer, which is -(3/2).
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The sum of the series (1/2) + (1/3) + (1/6) + .... upto 9 terms isa)(-5/6)b)-(1/2)c)1d)-(3/2)Correct answer is option 'D'. Can you explain this answer?
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