Arithmetic sequence or geometric sequence?
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Arithmetic sequence or geometric sequence?

[From: ] [author: ] [Date: 14-05-26] [Hit: ]
A geometric sequence has a constant multiplier. The sequence 2 + 6 + 12 + 20 + 60 + .........
What kind of sequence is this?

1*2+2*3+3*4+....+2013*2014

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Well,

Neither.

the sum S = 1*2+2*3+3*4+....+2013*2014

is a FINITE sum then can be easily computed : this is one one the good points with computers (or Excel macros)

comment from a physical :
2013 is ~ 2*10^3 so 2013*2014 is ~ 2*10^(6000)

and the astrophysician evaluate to 10^80 the number of material atoms in the UNIVERSE...

means S is really... really... a fictional number...

michael

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To find the sum
It's the sum of i*(i + 1)= i^2+i

The sum of i^2 from 1 to n is n(n+1)(2n+1)/6
The sum of i from 1 to n is n(n+1)/2

Adding the two together you can factor out n(n+1) to get
N(n+1)[(2n+1)/6 + 1/2]= n(n+1)[(2n+1)/6+3/6]
n(n+1)(2n+4)/6= n(n+1)(n+2)/3

Now plug in 2013 for n to get the sum

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Neither. An arithmetic sequence has a constant difference. A geometric sequence has a constant multiplier. The sequence 2 + 6 + 12 + 20 + 60 + ...does not match either definition
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keywords: geometric,sequence,or,Arithmetic,Arithmetic sequence or geometric sequence?
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