Tổng quát: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

Ta có: \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)

1/6+1/12+1/20+1/30+1/42+1/56=3/8

1/6+1/12+1/20+1/30+1/42+1/56

=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

=1/2-1/8

=3/8

\(D=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{100^2}-1\right)\)

\(=-\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)....\left(1-\frac{1}{100^2}\right)\)

\(=-\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}.....\frac{100^2-1}{100^2}\)

\(=-\left(\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}....\frac{99.101}{100^2}\right)\)

\(=-\left(\frac{1.2.3...99}{2.3.4...100}.\frac{3.4.5...101}{2.3.4....100}\right)\)

\(=-\left(\frac{1}{100}.\frac{101}{2}\right)\)

\(=-\frac{101}{200}\)

\(D=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)\cdot\cdot\cdot\left(\frac{1}{100^2}-1\right)\)(có 50 số hạng)

\(\Rightarrow D=\left(\frac{2^2-1}{2^2}\right)\left(\frac{3^2-1}{3^2}\right)\cdot\cdot\cdot\left(\frac{100^2-1}{100^2}\right)\)

\(\Rightarrow D=\frac{1\cdot3}{2^2}\cdot\frac{2\cdot4}{3^2}\cdot\cdot\cdot\frac{99\cdot101}{100^2}\)

\(\Rightarrow D=\frac{101}{2\cdot100}=\frac{101}{200}\)

1/2+3/5+1/9+1/127+7/18+4/35+2/7

=(1/2+1/9)+(3/5+2/7)+1/127+7/18+4/35

=11/18+31/35+1/127+7/18+4/35

=(11/18+7/18)+(31/35+4/35)+1/127

=1+1+1/127

=2+1/127

=2\(\frac{1}{127}\)

=

Minh ngoc oi minh giu nguyen ket qua la hon so a

cậu phải tích cho tô trước cái đã thì tớ giải cho tớ hứa

giai di roi kick sau

di zui giai cho

3-2 + 7 x 5-1 + 7 + 7 + 8 + 8 + 9 

= 1 + 35 - 1 + 14 + 16 + 9

= 10 + 35 - 1 + 30

= 40 + 35 - 1 = 74

Chuẩn không dùng máy tính nhóe

3-2+7x5-1+7+7+8+8+9 = 74 

đáp án : 74

=74 nha

nhân cả cụm đó với 2 rồi trừ đi cụm ban đầu thì còn là -2-1/1024 =-2049/1024

nhanh nhanh nhanh

tui trả lời rồi đó tck đi

- 246

- 908

890

-123-123=123+(-123)=0

-456-123+123-452=(-456)-[(-123)+123]-452

=(-456)-0-452

=(-456)-452

=--908

-789-(-421)+1258

=(-789)+421+1258

=(-368)+1258=890

tik nha

\(A=\left(1-\frac{1}{12}\right)\left(1-\frac{1}{13}\right)\left(1-\frac{1}{14}\right)...\left(1-\frac{1}{18}\right)\)

    \(=\frac{11}{12}.\frac{12}{13}.\frac{13}{14}...\frac{17}{18}\)

      \(=\frac{11}{18}\)     

   \(_{\left(1-\frac{1}{12}\right)\times\left(1-\frac{1}{13}\right)\times\left(1-\frac{1}{14}\right)\times\left(1-\frac{1}{15}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{17}\right)\times\left(1-\frac{1}{18}\right)}\)

= \(_{\frac{11}{12}\times\frac{12}{13}\times\frac{13}{14}\times\frac{14}{15}\times\frac{15}{16}\times\frac{16}{17}\times\frac{17}{18}}\)

=\(_{\frac{11\times12\times13\times14\times15\times16\times17}{12\times13\times14\times15\times16\times17\times18}}\)

=\(_{\frac{11}{18}}\)