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Bunuel
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What is the value of: 1/3[(1/2 - 1/5)+(1/3-1/6)+(1/4-1/7)+...] ? 21 Jan 2022, 07:45
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45% (medium)

Question Stats:

72% (02:19) correct 28% (02:32) wrong based on 323 sessions

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What is the value of: \(\frac{1}{3}[(\frac{1}{2} - \frac{1}{5})+(\frac{1}{3}-\frac{1}{6})+(\frac{1}{4}-\frac{1}{7})+...]\), where both denominators in successive terms increased by 1?


(A) \(\frac{11}{19}\)

(B) \(\frac{13}{36}\)

(C) \(\frac{29}{49}\)

(D) \(\frac{31}{43}\)

(E) \(\frac{49}{59}\)
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B
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What is the value of: 1/3[(1/2 - 1/5)+(1/3-1/6)+(1/4-1/7)+...] ? 21 Jan 2022, 08:52
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Answer B

Explanation below
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Ankur17000
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What is the value of: 1/3[(1/2 - 1/5)+(1/3-1/6)+(1/4-1/7)+...] ? 09 Sep 2024, 05:41
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Bunuel
What is the value of: \(\frac{1}{3}[(\frac{1}{2} - \frac{1}{5})+(\frac{1}{3}-\frac{1}{6})+(\frac{1}{4}-\frac{1}{7})+...]\), where both denominators in successive terms increased by 1?


(A) \(\frac{11}{19}\)

(B) \(\frac{13}{36}\)

(C) \(\frac{29}{49}\)

(D) \(\frac{31}{43}\)

(E) \(\frac{49}{59}\)
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­The denominator has to be divisible by 3. Only B can be the answer.
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What is the value of: 1/3[(1/2 - 1/5)+(1/3-1/6)+(1/4-1/7)+...] ? 09 Sep 2024, 21:59
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Is there any other way to solve this question?
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What is the value of: 1/3[(1/2 - 1/5)+(1/3-1/6)+(1/4-1/7)+...] ? 11 Sep 2024, 09:50
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lavanya.18
Is there any other way to solve this question?
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­Here is how I found the answer, hope other members will tell me if I make sense:

Calculating 1/2 - 1/5 and the following fractions all give denominators that are even numbers, can't find a logical link between the pacing of their denominators but for sure we can see they are even numbers so adding them will give an even number in the parenthesis.

Well, Even x odd = Even, example: 2 x 3 = 6.

1/3 will multiply the whole parenthesis, the denominator being 3 (odd), so without much calculation needed again i know that for sure the denominator of the result has to be even. Only B gives us an even denominator, the rest are all odd numbers so it doesn't make sense, so here is the answer.

Answer B.
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What is the value of: 1/3[(1/2 - 1/5)+(1/3-1/6)+(1/4-1/7)+...] ? 03 Jun 2026, 05:43
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