minh nhanh

\(B=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)

\(B=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{11\cdot12}\)

\(B=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\)

\(B=\frac{1}{4}-\frac{1}{12}\)

\(B=\frac{1}{6}\)

Tính nhanh : 

B = 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132 

B = 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12

B = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ...... + 1/11 - 1/12

B = 1/4 - 1/12

B = 3/12  - 1/12

B = 2/12

B = 1/6 

=1/3*5+1/5*7+1/7*9+...+1/99*101

=1/3-1/5+1/5-1/7+...+1/99-1/101

=1/3-1/101

=98/303

1/15 + 1/35 + 1/63 + 1/99 + ... + 1/9999 

= 1/(3x5) + 1/(5x7) + 1/(7x9) + ... + 1/(99x101)

= (1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ...+ 1/99 - 1/101) : 2

= (1/3 - 1/101) : 2 

= 98/303 : 2

= 49/303

\(a=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+....+\frac{1}{9999}\)

\(a=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{99.101}\)

\(a=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-....-\frac{1}{101}\right)\)

\(a=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{101}\right)=\frac{49}{303}\)

Ta có : (1 - 1/3) x (1 - 1/4) x ... x (1 - 1/99)

= 2/3 x 3/4 x ... x 98/99

= 2/99 (Rút gọn)

Vậy A = 2/99

bằng 2/99

Cố lên nha ae

Ta có: \(A=\frac{10^{19}+1}{10^{20}+1}\Rightarrow10A=\frac{10^{20}+10}{10^{20}+1}=1+\frac{9}{10^{20}+1}\)

\(B=\frac{10^{20}+1}{10^{21}+1}\Rightarrow10B=\frac{10^{21}+10}{10^{21}+1}=1+\frac{9}{10^{21}+1}\)

Vì \(\frac{9}{10^{20}+1}>\frac{9}{10^{21}+1}\Rightarrow1+\frac{9}{10^{201}+1}>1+\frac{9}{10^{21}+1}\Rightarrow10A>10B\)

\(\Rightarrow A>B\)

Vậy A > B

Ta có: nếu \(\frac{a}{b}< 1\) thì \(\frac{a}{b}< \frac{a+n}{b+n}\left(n\in N\right)\)

\(B=\frac{10^{20}+1}{10^{21}+1}< \frac{10^{20}+1+9}{10^{21}+1+9}=\frac{10^{20}+10}{10^{21}+10}=\frac{10\left(10^{19}+1\right)}{10\left(10^{20}+1\right)}=\frac{10^{19}+1}{10^{20}+1}=A\)

Vậy A > B

1 + 1 + 1 = 3

1+1+1=3

1+1+1=3

(1/2+1/8)+(1/4+1/16)+(1/8+1/32)+1/64

=1/10+1/20+1/40+1/64

=61/320

lấy 1/64 làm mẫu xố chung

1/64+2/64+4/64+8/64+12/64+32/64=59/64

MTC: 64

=> \(\frac{32}{64}+\frac{16}{64}+\frac{8}{64}+\frac{4}{64}+\frac{2}{64}+\frac{1}{64}\)

= \(\frac{63}{64}\)

1 + 1 + 1 + 1 + 1+ 1 + 1+ 1 +1 +1 = 10

Giải rõ nha

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

1/2 +1/(2.3) +1/(3.4) + 1/(4.5) + 1/(5.6) + 1/(6.7) 
=(2-1)/2 + (3-2)/(2.3) +(4-3)/(3.4) + (5-4)/(4.5) + (6-5)/(5.6) + (7-6)/(6.7) 
=1-1/2 +1/2-1/3+....+1/6-1/7 
=1-1/7 
=6/7

đặt biểu thức trên là A

\(\Rightarrow A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{6.7}\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+....+\frac{7-6}{6.7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}=\frac{6}{7}\)

      \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}\)

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

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)