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If s1, s2, s3, ...... is the sequence such that Sn=n/(n+1)

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If s1, s2, s3, ...... is the sequence such that Sn=n/(n+1)  [#permalink]

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New post 01 Sep 2008, 11:31
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If s1, s2, s3, ...... is the sequence such that Sn=n/(n+1) for all positive integers n, then the product of the first 10 terms of this sequence is.

(A) 1/(10*11) (B) 1/11
(C) 1/10 (D) 9/10
(E) 10/11


in other words what is the product of 1/2*2/3*3/4*.....................10/11

please give details to your explanation.

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Re: PS sequence [#permalink]

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New post 01 Sep 2008, 12:05
if s1, s2, s3, ...... is the sequence such that Sn=n/(n+1) for all positive integers n, then the product of the first 10 terms of this sequence is.

(A) 1/(10*11) (B) 1/11
(C) 1/10 (D) 9/10
(E) 10/11


first number will be S1 = 1/2
S2 = 2/3
.....
......
10th number will be S10 = 10/11

product of 10 numbers will be 1/2*2/3*.............9/10*10/11
= 1/11

and product for n terms will be 1/n+1
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Manager
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Re: PS sequence [#permalink]

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New post 01 Sep 2008, 12:10
hksingh83 wrote:
if s1, s2, s3, ...... is the sequence such that Sn=n/(n+1) for all positive integers n, then the product of the first 10 terms of this sequence is.

(A) 1/(10*11) (B) 1/11
(C) 1/10 (D) 9/10
(E) 10/11


first number will be S1 = 1/2
S2 = 2/3
.....
......
10th number will be S10 = 10/11

product of 10 numbers will be 1/2*2/3*.............9/10*10/11
= 1/11

and product for n terms will be 1/n+1


Why "and product for n terms will be 1/n+1"

is this a formula or something?

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Re: PS sequence [#permalink]

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New post 01 Sep 2008, 12:16
if you see the series it goes like this

1/2 , 2/3, 3/4........n-1/n+1, n/n+1

you can see the denominator of the present term is numerator of next consecutive term

so while taking product it is just canceled
and the left is first term numerator and the last term denominator

please verify
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Re: PS sequence [#permalink]

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New post 01 Sep 2008, 15:01
hksingh83 wrote:
if you see the series it goes like this

1/2 , 2/3, 3/4........n-1/n+1, n/n+1

you can see the denominator of the present term is numerator of next consecutive term

so while taking product it is just canceled
and the left is first term numerator and the last term denominator

please verify


very elegant, how did i not see it?
thank you again.

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Re: PS sequence   [#permalink] 01 Sep 2008, 15:01
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If s1, s2, s3, ...... is the sequence such that Sn=n/(n+1)

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