Question

Tính tổng:

\(y=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+....+\frac{1}{998\cdot999\cdot1000}\)

Giải kĩ ra nhé, mình đang cần gấp, mình sẽ tick cho

Answer 1

2y= 2/ 1.2.3 + 2/2.3.4 + 2/3.4.5 +.... +2/998.999.1000

2y=1/1.2 - 1/2.3 +1/2.3 - 1/3.4 + 1/3.4 -1/4.5 +....+ 1/998.999 - 1/ 999.1000

2y=1/2 - 1/ 999.1000

2y = 499500-1 /  999.1000

2y=499499 / 999.1000

y=499499 / 1998000

Ủng hộ mk nha

Answer 2

bai toan nay khó quá

Answer 3

Ta có : \(2Y=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+.....+\frac{2}{998.999.1000}\)

\(\Rightarrow2Y=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{998.999}-\frac{1}{999.1000}\)

\(\Rightarrow2Y=\frac{1}{1.2}-\frac{1}{999.1000}=\frac{1}{2}-\frac{1}{999000}=\frac{499499}{999000}\)

\(\Rightarrow Y=\frac{499499}{999000}\div2\)