\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
Mk ghi hơi ngắn nên mong bn sẽ hiểu.
CHÚC BẠN HỌC TỐT!
Trả lời
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{99\cdot100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
Có: \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
1/2-1/3+1/3-1/4+...+1/99-1/100=1/2-1/100=49/100
1/2.3 + 1/3.4 + ... + 1/99.100
= 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100
= 1/2 + (-1/3 + 1/3) + (-1/4 + 1/4) + ... + (-1/99 + 1/99) - 1/100
= 1/2 - 1/100 = 49/100
1/2-1/3+1/3-1/4+....+1/98-1/99+1/99-1/100 =1/2 -1/100 =49/100
3-2/2.3+4-3/3.4+....+100-99/99.100
=1/2-1/3+1/3+...+1/99-1/100
=1/2-1/100
=49/100