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Simplify (1+3+5+...+199)/(2+4+6+...+198+200+202).

 Jul 29, 2022
 #1
avatar+197 
0

1 + 3 + .... + (2n - 1) = n^2

 

2n - 1 = 199

2n = 200

n = 100

 

10000 * 2(1 + 2 + 3....  + 101) 

= 10000 * 2(5151) 

= 10000 * 10302 

= 103020000

 Jul 29, 2022
 #2
avatar+2322 
0

https://web2.0calc.com/questions/simplify-1-3-5-199-2-4-6-200-202

 Jul 29, 2022
 #3
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Simplify (1+3+5+...+199) / (2+4+6+...+198+200+202)==[2n - 1] / [2n] ==10,000 / 10,302


5,000 / 5,151

 Jul 29, 2022
 #4
avatar+124524 
+2

1 + 3 +  ....+ 199

 

Number of terms    =   (199 - 1)  / 2  + 1    =  100

 

Sum  =   (1 + 199) / ( 100 / 2)  =   10000

 

 

2 + 4 + ......+ 202

 

Number of terms =   (200 - 2) / 2 + 1 =   101

 

Sum =  (2 + 202)  * (101) /2  =  10302

 

10000 /  10302  =   5000 / 5151

 

 

cool cool cool

 Jul 29, 2022
 #5
avatar+197 
0

Sorry, I thought it was a multiplication sign! Woops!

 Jul 30, 2022

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