Question

[Lưu Quang Dũng]

giúp mình với, cần gấp!!!

Answer 1

[nguyễn thị kim phượng]

a)1/1.2+1/2.3+1/3.4+....+1/1999.2000

=1-1/2+1/2-1/3+1/3-1/4+....+1/1999-1/2000

=1-1/2000

= Bn tự tính

b)=1/3.(1/1.4+1/4.7+1/7.10+...+1/100+103)

=1/3.(1-1/4+1/4-1/7+1/7-1/10+...+1/100-1/103)

=1/3.(1-1/103)

= tự làm

c)8/9-1/72-1/56-1/42-...-1/6-1/2

=8/9-(1/2+1/6+...+1/42+1/56+1/72)

=làm tương tự phần trên. Gợi ý :72=8.9 . Nói đến thế r mà ko bt làm thì chịu. yên tâm, đảm bảo đ, t học đội tuyển mà

Answer 2

[Đoàn Đức Hà]

a) \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1999.2000}\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{2000-1999}{1999.2000}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1999}-\frac{1}{2000}\)

\(=1-\frac{1}{2000}=\frac{1999}{2000}\)

b) \(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{100.103}\)

\(=\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{100.103}\right)\)

\(=\frac{1}{3}\left(\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+...+\frac{103-100}{100.103}\right)\)

\(=\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\right)\)

\(=\frac{1}{3}\left(1-\frac{1}{103}\right)\)

\(=\frac{34}{103}\)

c) \(\frac{8}{9}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{8}{9}-\left(\frac{1}{8.9}+\frac{1}{7.8}+...+\frac{1}{2.3}+\frac{1}{1.2}\right)\)

\(=\frac{8}{9}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

\(=\frac{8}{9}-\left(1-\frac{1}{9}\right)=0\)