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The sequence S is defined as follows for all n ≥ 1: The sum of the

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GeminiHeat
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The sequence S is defined as follows for all n ≥ 1: The sum of the [#permalink] New post   09 Jul 2021, 08:01
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The sequence S is defined as follows for all n ≥ 1:

\(S_n=(-1)^n*\frac{1}{n(n+1)}\)

The sum of the first 10 terms of S is:

(A) Between –1 and –1/2

(B) Between –1/2 and 0

(C) Between 0 and 1/2

(D) Between 1/2 and 1

(E) Greater than 1
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GeminiHeat
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Re: The sequence S is defined as follows for all n ≥ 1: The sum of the [#permalink] New post   17 Jul 2021, 23:23
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+1 Kudos to posts containing answer with explanation
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Re: The sequence S is defined as follows for all n ≥ 1: The sum of the [#permalink] New post   07 Sep 2021, 06:56
GeminiHeat wrote:
The sequence S is defined as follows for all n ≥ 1:

\(S_n=(-1)^n*\frac{1}{n(n+1)}\)

The sum of the first 10 terms of S is:

(A) Between –1 and –1/2

(B) Between –1/2 and 0

(C) Between 0 and 1/2

(D) Between 1/2 and 1

(E) Greater than 1


Could someone please explain their approach
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The sequence S is defined as follows for all n ≥ 1: The sum of the [#permalink] New post   07 Sep 2021, 07:14
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S1 = -1/2
S2 = 1/6
S3 = -1/12
S4 = 1/20 .....

Neglecting the remaining terms as fractions does not vary the sum more than 1%.

S=S1+S2+S3+S4...S10 > -1/3, but S<-1/4 .

-1/3 <S< -1/4. So answer falls in B.
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The sequence S is defined as follows for all n ≥ 1: The sum of the [#permalink]
07 Sep 2021, 07:14
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