Question

TÍNH:

A = \(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)+\(\frac{2}{4.5}\)+.....+\(\frac{2}{99.100}\)

Answer 1

\(A=\frac{2}{2}-\frac{2}{3}+\frac{2}{3}-\frac{2}{4}+\frac{2}{4}-\frac{2}{5}+\frac{2}{5}-\frac{2}{6}+.....+\frac{2}{99}-\frac{2}{100}\)

Ta tính các số âm và số dương giống nhau cộng lại có tổng bằng 0

\(\Rightarrow A=\frac{2}{2}-\frac{2}{100}\)

\(A=\frac{100}{100}-\frac{2}{100}=\frac{98}{100}=\frac{49}{50}\)

Đúng 100%

Đúng 100%

Đúng 100%

Answer 2

\(A=\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+....+\frac{2}{99\cdot100}\)

\(A:2=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{99\cdot100}\)

A : 2 = \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{99}-\frac{1}{100}\)

\(A:2=\frac{1}{2}-\frac{1}{100}\)

\(A:2=\frac{49}{100}\)

       A  = \(\frac{49}{50}\)

Answer 3

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{99.100}\)

\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(A=2.\frac{49}{100}\)

\(A=\frac{49}{50}\)

Answer 4

A = 2/2.3 + 2/3.4 + 2/4.5 +......+ 2/99.100

A = 2.( 1/2.3 + 1/3.4 + 1/4.5 +.......+ 1/99.100 )

A = 2.( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +......+ 1/99 - 1/100 )

A = 2.( 1/2 - 1/100 )

A = 2.49/100

A = 49/50

tk mk nhé

Answer 5

^{\(\frac{2}{2.3}\)}+...+\(\frac{2}{99.100}\)=2.(\(\frac{1}{2}\)-\(\frac{1}{3}\) +...+\(\frac{1}{99}\) -\(\frac{1}{100}\) )

                                    =2.(\(\frac{1}{2}\) -\(\frac{1}{100}\) )

                                    =2.\(\frac{49}{100}\) 

                                  =\(\frac{49}{50}\) 

h cho minh nha