Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{66}\)
\(\frac{A}{2}=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{132}\)
\(\frac{A}{2}=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{11\cdot12}\)
\(\frac{A}{2}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{11}-\frac{1}{12}\)
\(\frac{A}{2}=\frac{1}{4}-\frac{1}{12}\)
\(\Rightarrow A=\frac{2}{4}-\frac{2}{12}=\frac{16}{48}\)
\(B=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{55}\)
\(\frac{B}{2}=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{110}\)
\(\frac{B}{2}=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{10\cdot11}\)
\(\frac{B}{2}=\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\)
\(\frac{B}{2}=\frac{1}{3}-\frac{1}{11}\)
\(\Rightarrow B=\frac{2}{3}-\frac{2}{11}=\frac{16}{33}\)
Mà \(\frac{16}{48}< \frac{16}{33}\Rightarrow A< B\)
Vậy : A < B
\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+....+\frac{1}{55}\)
=\(\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+....+\frac{2}{110}\)
=\(2.\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{10.11}\right)\)
=\(2.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+..+\frac{1}{10}-\frac{1}{11}\right)\)
= \(2.\left(\frac{1}{3}-\frac{1}{11}\right)\)
=\(2.\frac{8}{33}\)
= \(\frac{16}{33}\)
\(A=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{55}\) => \(\frac{A}{2}=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{110}=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{10.11}\)
=> \(\frac{A}{2}=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{10}-\frac{1}{11}=\frac{1}{3}-\frac{1}{11}=\frac{8}{33}\)
=> \(A=\frac{16}{33}\)
A = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + ..+ \(\dfrac{1}{55}\)+ \(\dfrac{1}{66}\)
A = 2 \(\times\) ( \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) +...+ \(\dfrac{1}{110}\) + \(\dfrac{1}{132}\))
A = 2 \(\times\) ( \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\)+ \(\dfrac{1}{5.6}\) +...+ \(\dfrac{1}{10.11}\)+ \(\dfrac{1}{11.12}\))
A = 2 \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\) +...+ \(\dfrac{1}{10}\) - \(\dfrac{1}{11}\)+ \(\dfrac{1}{11}\) - \(\dfrac{1}{12}\))
A = 2 \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{12}\))
A = 1 - \(\dfrac{1}{6}\) < 1
Vậy A = \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + ...+ \(\dfrac{1}{55}\)+ \(\dfrac{1}{66}\) < 1
Bài 1:
1: =15+37+52-37-17=52-2=50
2: =38-42+14-25+27+15=62-42+29=20+29=49
Bài 1: Bỏ ngoặc rồi tính
3) (21-32) - (-12+32)=21-32-(-12)-32=21-32+12-32=-31
4) (12+21) - (23-21+10)=12+21-23+21-10=21
5) (57-725) - (605-53)=57-725-605+53=-1220
6) (55+45+15) - (15-55+45)=55+45+15-15+55-45=55+55=110
Bài 2: Tính các tổng sau một cách hợp lí
1) (-37) + 14 + 26 + 37=(-37+37)+(14+26)=0+40=40
2) (-24) +6 + 10 + 24=(-24+24)+(6+10)=0+16=16
3) 15 + 23 + (-25) + (-23)=(15-25)+(23-23)=-10+0=-10
4) 60 + 33 + (-50) + (-33)=(60-50)+(33-33)=10+0=10
5) (-16) + (-209) + (-14) + 209=(-16-14)+(-209+209)=-30+0=-30
6) (-12) + (-13) + 36 + (-11)=(-11-12-13)+36=-36+36=0
A =\(2.\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+......+\dfrac{1}{156}\right)\)
A =\(2.\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+..........+\dfrac{1}{12.13}\right)\)
A =2.\(\left(\dfrac{1}{3}-\dfrac{1}{13}\right)\)
A=\(2.\dfrac{10}{39}=\dfrac{20}{39}\)
Số thứ 3 : 1 + 2 + 3 = 6
Số thứ 4 : 1+2+3+4 = 10
Số thứ 5 : 1+2+3+4+5 = 15
........................................
Số thứ 100 : 1 + 2 + 3 + 4 + ...+ 100
Théo cách tính tổng dãy số cách đều :
1 + 2 + 3 + 4 + ...+ 100 = (1+100) x 100 : 2 = 5050
nhan ca tu va mau cho 2 sau đó đặt nhân tử chung là 2 ta được
đề = 2(1/20 + 1/30 + 1/42+ 1/56+1/72+1/90+1/110+1/132)
= 2[1/(4.5) +1/(5X6) + 1/(6X7) + 1/(7x8) + 1/(8x9) + 1/(9x10)+ 1/(10x11) + 1/(11x12)]
biến đổi : 1/(4x5) = 1/4 - 1/5....tương tự ta được
= 2[(1/4 - 1/5 ) + (1/5-1/6) + (1/6-1/7) +(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10 - 1/11)+ (1/11-1/12)]
mo ngoac rut gon het lại
= 2(1/4 - 1/12) = 1/3