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Sequence Term and Sum (Posted on 2013-09-20) Difficulty: 3 of 5
Define the sequence An  as:     
       n, if n is odd
An =   0, if n = 4t-2 
       1, if n = 4t
whenever t is a positive integer.
Derive a one-line expression for each of the following:

(i) An in terms of n

(ii) Sn in terms of n, where Sn denotes the sum of all the terms of An

No Solution Yet Submitted by K Sengupta    
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solution Comment 1 of 1

 

The n-th term: 

 

a(n)=n* KD(n mod2,1) + KD(n mod4,0) 

 

**for definition of KD(Kronecker delta) see:

  http://reference.wolfram.com/mathematica/ref/KroneckerDelta.html 

 

 

Checking: 

 

a(17)=17 

a(18)=0 

a(19)=19 

a(20)=1

 

And the sum of n terms is: 

S(n)=Sum(a(1) to a(n)))= INT((N+1)/2)^2+ INT(N/4) <br>


 Checking: S(11)=6^2+2=38

 1+0+3+1+5+0+7+1+9+0+11=38

Edited on September 20, 2013, 3:31 pm
  Posted by Ady TZIDON on 2013-09-20 15:27:22

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