\(\frac{5}{2\cdot4}+\frac{5}{4\cdot6}+\frac{5}{6\cdot8}+.....+\frac{5}{48\cdot60}\)

\(=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{48}-\frac{1}{50}\right)\)

\(=\frac{5}{2}\left(\frac{1}{2}-\frac{1}{50}\right)\)

Tự tính nốt :p

theo công thức 1/n x 1 = 1/n - 1/1  mà làm

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

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

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

\(=98\times100\times102\)

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

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

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

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

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

\(=98\times100\times102\)

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

2/2x4+ 2/4x6+ 2/6x8+...+2/2014x2016

=1/2-1/4+1/4-1/6+1/6-1/8+...+1/2014-1/2016

=1/2-1/2016

=1008/2016-1/2016

=1007/2016

\(\frac{2}{2x4}+\frac{2}{4x6}+\frac{2}{6x8}+...+\frac{2}{2014x2016}\)

\(=\frac{4-2}{2x4}+\frac{6-4}{4x6}+\frac{8-6}{6x8}+...+\frac{2016-2014}{2014x2016}\)

\(=\frac{4}{2x4}-\frac{2}{2x4}+\frac{6}{4x6}-\frac{4}{4x6}+\frac{8}{6x8}-\frac{6}{6x8}+...+\frac{2018}{2016x2018}-\frac{2016}{2016x2018}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(=\frac{1}{2}-\frac{1}{2018}\)

\(=\frac{504}{1009}\)

1/2.4 + 1/4.6 + 1/6.8 + ... + 1/96.98 + 1/98.100

= 1/2.(2/2.4 + 2/4.6 + 2/6.8 + ... + 2/96.98 + 2/98.100)

= 1/2.(1/2 - 1/4 + 1/4 - 1/6 + ... + 1/96 - 1/98 + 1/98 - 1/100)

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

= 1/2.49/100

= 49/200

49/200

duyệt đi

kết quả bằng 49/200