Question

Aratati ca A este congruent cu [0,(3);0,5] Unde

a=1/2x3+1/3x4+1/4x5+....1/29x30

Answer 1

a = 1/2x3+1/3x4+1/4x5+... + 1/29x30

a = (3-2)/2×3 + (4-3)/3×4 + (5-4)/4×5 +...+ (30-29)/29×30

a = 3/2×3 - 2/2×3 + 4/3×4 - 3/3×4 + 5/4×5 - 4/4×5 +...+ 30/29×30 - 29/29 × 30

facem simplificarile si ne ramane

a = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5+ ... + 1/29 - 1/30

se reduc termenii asemenea care sunt cu (+) si cu (-) si ne ramane

a = 1/2 - 1/30

a = (15 - 1)/30

a = 14/30

a = 0,4(6) se afla in intervalul [ 0,(3); 0,5]
________________________________




0 0,1 0,2 0,3 0,4 0,5 1
|___|___|___|___|___|___|___|___|___|___|