Question

E=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+.........+\frac{1}{86.87.88}\)

Ai tìm ra cấu trả lời dc tik điểm nha

 

Answer 1

Từ giả thiết suy ra:

2E=\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+..+\frac{2}{86.87.88}\)

2E=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{86.87}+\frac{1}{87.88}\)

2E=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{86}-\frac{1}{87}+\frac{1}{87}-\frac{1}{88}\)

2E=\(1-\frac{1}{88}\)

2E=\(\frac{87}{88}\)

E=\(\frac{87}{176}\)

Vậy E=\(\frac{87}{176}\)