Question

Aflati x :

x = (1/2 + 1/3 + 1/4 +...+ 1/2017) / (2016 - 1/2 - 2/3 - 3/4 - ... - 2016/2017)

Mulțumesc !!!

Answer 1

O sa rezolv prima oara numitorul :

2016 - 1/2 - 2/3 - 3/4 -...- 2016/2017 =

2016 - (1/2 + 2/3 + 3/4 +...+ 2016/2017) =

2016 - (2/2 - 1/2 + 3/3 - 1/3 + 4/4 - 1/4 +...+ 2017/2017 - 1/2017 =

2016 - ( 1 - 1/2 + 1 - 1/3 + 1 - 1/4 + ...+ 1 - 1/2017) =

2016 - [ 1 + 1 + 1+ ...+ 1 de 2016 ori - (1/2 + 1/3 + 1/4 +...+ 1/2017)] =

2016 - [ 1 × 2016 - (1/2 + 1/3 + 1/4 +...+ 1/ 2017)] =

2016 -2016 + (1/2 + 1/3 + 1/4 + ...+ 1/2017) =

1/2 + 1/3 + 1/4 +...+ 1/2017 (numitorul)

x = (1/2 + 1/3 + 1/4 + ...+ 1/2017) / (1/2 + 1/3 + 1/4 +...+ 1/2017)

x = 1
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