Question

Fie n=(5+10+15+...+275) (1/1×6+1/6×11+1/11×16+...+1/51×56).Aratati ca 2n este patrat perfect.
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Answer 1

n=(5+10+15+...+275) (1/1×6+1/6×11+1/11×16+...+1/51×56)

n=5(1+2+3+….+55)( 1/1×6+1/6×11+1/11×16+...+1/51×56)

n=(55•56/2)•( 5/1×6+5/6×11+5/11×16+...+5/51×56)

2n=55•56•(1/1-1/6+1/6-1/11+1/11-1/16+…..+1/51-1/56)

2n=55•56•(1/1-1/56)

2n=55•56•55/56

2n=55²,  este patrat perfect