\(D=\frac{6}{2x4}+\frac{6}{4x6}+\frac{6}{6x8}+....+\frac{6}{48x50}\)

\(=\frac{6}{2}x\left(\frac{2}{2x4}+\frac{2}{4x6}+\frac{2}{6x8}+....+\frac{2}{48x50}\right)\)

\(=3x\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+....+\frac{1}{48}-\frac{1}{50}\right)\)

\(=3x\left(\frac{1}{2}-\frac{1}{50}\right)=3x\frac{12}{25}=\frac{36}{25}\)

Vậy D=36/25

D=6/2x4 + 6/4x6 + 6/6x8 + ...+ 6 /48 x50

D=3 x (2/2x4 + 2/4x6 +  2/6x8 + ...+ 2 /48 x50)

D= 3x (1/2 - 1/4 + 1/4 - 1/6 + 1/6-1/8 + ... + 1/48 - 1/50)

D= 3 x (1/2 - 1/50)

D= 3 x 12/25

D= 36/25

\(A=2\times4+4\times6+6\times8+...+98\times100\)

\(6\times A=2\times4\times6+4\times6\times\left(8-2\right)+6\times8\times\left(10-4\right)+...+98\times100\times\left(102-96\right)\)

\(=2\times4\times6+4\times6\times8-2\times4\times6+6\times8\times10-4\times6\times8+...+98\times100\times102-96\times98\times100\)

\(=98\times100\times102\)

\(\Leftrightarrow A=\frac{98\times100\times102}{6}=166600\)

166600 nha

Câu hỏi tương tự nha
= 2 x ( 2 + 2 ) + 4 x ( 2 + 2 ) + 6 x ( 2 +2 ) +....+98 x ( 98 + 2 )
= 2 x 2 + 2 x 2 + 2 x 4 +4+......+98 x 98 = 2 x 98
= 2 x ( 2 + 4 + 6 +....+98 ) +( 2 x 2 + 4x4 + 6 x 6 +...+98 x 98 )
= 2 x 2450 + 40425 x 4
= 4900 + 161700 = 166600

Gọi biểu thức trên là A ta có:

Zô câu hỏi tương tự là cách giải

ĐS A = 49/200

Gọi biểu thức trên là A, ta có:

A=1/(2x4) + 1/(4x6) + 1/(6x8) + ... + 1/(96x98) + 1/(98x100) 

2A=2/(2x4) + 2/(4x6) + 2/(6x8) + ... + 2/(96x98) + 2/(98x100) 

2A=1/2-1/4+1/4-1/6+1/6-1/8+...+1/96-1/98+1/98-1/100

giản ước đi, ta có:

2A=1/2-1/4+1/4-1/6+1/6-1/8+...+1/96-1/98+1/98-1/100

2A=1/2-1/100

2A=49/100

=>A=49/100:2

=>A=49/200

zồi tick nhé

S=(2+98)*(4+6)+...+100+100+102

100*10+....+100+100*102
=224400

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

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

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

Ta có:

\(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+....+\frac{1}{98.100}\)

\(\Rightarrow2A=\frac{2}{2.4}+\frac{2}{4.6}+....+\frac{2}{98.100}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\)

\(\Rightarrow2A=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

\(\Rightarrow A=\frac{49}{100}\div2=\frac{49}{200}\)

Vậy giá trị của biểu thức là \(\frac{49}{200}\)

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)

= \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

= \(\frac{1}{2}-\frac{1}{100}\)

= \(\frac{49}{100}\)

Ps: Tham khảo: [Toán nâng cao 5] - Tính nhanh phân số - tth - YouTube

\(E=2\times4+4\times6+6\times8+...+98\times100\)

\(6\times E=2\times4\times6+4\times6\times\left(8-2\right)+6\times8\times\left(10-4\right)+...+98\times100\times\left(102-96\right)\)

\(=2\times4\times6+4\times6\times8-2\times4\times6+...+98\times100\times102-96\times98\times100\)

\(=98\times100\times102\)

\(\Rightarrow E=\frac{98\times100\times102}{6}=166600\)

\(\frac{1}{2x4}\)+ \(\frac{1}{4x6}\)+ ... + \(\frac{1}{98x100}\)= \(\frac{1}{2}\)x(\(\frac{4-2}{2x4}\)+\(\frac{6-4}{4x6}\)+ ... + \(\frac{100-98}{98x100}\))

                                                        = \(\frac{1}{2}\)x(\(\frac{1}{2}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{8}\)+ ... + \(\frac{1}{98}\)-\(\frac{1}{100}\))

                                                        = \(\frac{1}{2}\)x(\(\frac{1}{2}\)-\(\frac{1}{100}\)) = \(\frac{49}{200}\)

kết quả là 49/50

49'/50

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{96.98}+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

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

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