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avatar+766 

Evaluate
2 + \frac{6}{7} +\frac {18}{49} + \frac{54}{343} + 1 + \frac{2}{14} + \frac{3}{98}.

 Mar 2, 2025

Best Answer 

 #2
avatar+130458 
+1

2+67+1849+54343+1+214+398

 

Rearrange as

 

1 + 2 + 6/7 + 2/14 + 18/49 + 54/343 + 3/98   = 

 

1 + 2 + (6/7 + 1/7)  +  18/49 + 54/343 + 3/98   = 

 

1 + 2 + 1  +   (126 + 54) / 343  +   (1.5) / 49   =

 

4  + 180/343  +  7(1.5) / 343   = 

 

4 + (180 / 343) + (10.5) /343  =

 

4 + (1800 + 105)  / 3430  

 

4 + 1905 /3430

 

4 + 381/686  =

 

3125 / 686

 

cool cool cool

 Mar 3, 2025
 #1
avatar+111 
+1

The sum of the series is

 over 49 end-fraction

229/49

.

 Mar 2, 2025
 #2
avatar+130458 
+1
Best Answer

2+67+1849+54343+1+214+398

 

Rearrange as

 

1 + 2 + 6/7 + 2/14 + 18/49 + 54/343 + 3/98   = 

 

1 + 2 + (6/7 + 1/7)  +  18/49 + 54/343 + 3/98   = 

 

1 + 2 + 1  +   (126 + 54) / 343  +   (1.5) / 49   =

 

4  + 180/343  +  7(1.5) / 343   = 

 

4 + (180 / 343) + (10.5) /343  =

 

4 + (1800 + 105)  / 3430  

 

4 + 1905 /3430

 

4 + 381/686  =

 

3125 / 686

 

cool cool cool

CPhill Mar 3, 2025

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