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KCC's Quizzes : AQQ234 - Sum of even integers



		

			

									
					    KCC
					
							

			
				
									
											
			
			
				
  •  Analog Employees  

			
			
			    	
			                    
                
				                on May 4, 2023 
				
			
			
		


				
		

		    		    
		    
		    	
			
The sum S of positive even integers starting from 2 to n (even) is described as :


                           S = 2 + 4 + 6 + 8 +… n where the last element n is even.


 Questions:


    

  1. What is the general formula (function of n) giving a such sum?
    2. 

  2. Give the sum with n = 5298
    3. 


										


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[edited by: emassa at 1:29 PM (GMT -4) on 5 May 2023]
				

						
			        
		


				
						
        

    
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    •  Analog Employees  
    
            
			                            
                                                                                                                        
            
				
			
            
					
    
	
    

		
		
    
					
    <NOPE, I BELIEVE THIS IS INCORRECT.  I need to go back and spend more time on this.>
    

    

    I'm noticing that the total given any n, call it T(n), is just n(n+1) as per below...
    

    


    
n
1
2
3
4
5

    

    
2n
2
4
6
8
10

    

    
T(n)
2
6
12
20
30

    

    
n(n+1)
2
6
12
20
30

    
    

    

    

    So, the formula is T(n) = n * (n+1)
    

    

    For n = 5298, T(n) = 5298 * 5299 = 28,074,102
    

    

    Not very scientific but I think it's correct.
    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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Reply

    


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    •  Analog Employees  
    
            
			                            
                                                                                                                        
            
				
			
            
					
    
	
    

		
		
    
					
    <NOPE, I BELIEVE THIS IS INCORRECT.  I need to go back and spend more time on this.>
    

    

    I'm noticing that the total given any n, call it T(n), is just n(n+1) as per below...
    

    


    
n
1
2
3
4
5

    

    
2n
2
4
6
8
10

    

    
T(n)
2
6
12
20
30

    

    
n(n+1)
2
6
12
20
30

    
    

    

    

    So, the formula is T(n) = n * (n+1)
    

    

    For n = 5298, T(n) = 5298 * 5299 = 28,074,102
    

    

    Not very scientific but I think it's correct.
    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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    •  Analog Employees  
    
            
			                            
                                                                                                                        
            
				
			
            
												
						in reply to brianb0722
					
									
    
	
    

		
		
    
					
    Hi Brian, 
    

    Thanks for your prompt reply.
    

    Well, I think you have been a little bit too fast. In effect the trick is you assume here n is the number of terms in the sequence while n is the last even integer in the sequence! For example for n=6, S should be 0+2+4+6 = 12 and not 6(6+1) = 42
    
			
    

		
			
	      

		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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