Tính nhanh
1, A = 1/1.2 + 1/2.3 + 1/3.4 + 1/3.4 + ... + 1/49.50
2, B = 2/3.5 + 2/5.7 + 2/7.9 + ... + 2/37.39
3, C = 5^2/1.6 + 5^2/6.11 + ... + 5/26.31
4, D = 1/7 + 1/91 + 1/247 + 1/475 + 1/775 + 1/1147
1, 1/7 + 1/91 + 1/247 + 1/475 + 1/775 + 1/1147
2, 1/6 + 5/6.7 + 1/7.8 + 5/8.9 + ... + 1/24.25
3, 22/5.7 + 22/7.9 + 22/9.11 + ... + 22/39.41
Cho\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
Cho \(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{775}+\frac{1}{1147}\)
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(S=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
\(S=5.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(S=5.\left(1-\frac{1}{31}\right)\)
\(S=5.\frac{30}{31}\)
\(S=\frac{150}{31}\)
Câu L bạn thiếu số\(\frac{1}{475}\)
\(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{475}+\frac{1}{775}+\frac{1}{1147}\)
\(L=\frac{1}{1.7}+\frac{1}{7.13}+\frac{1}{13.19}+\frac{1}{19.25}+\frac{1}{25.31}+\frac{1}{31.37}\)
\(L=\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}+\frac{6}{31.37}\right)\)
\(L=\frac{1}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+\frac{1}{19}-\frac{1}{25}+\frac{1}{25}-\frac{1}{31}+\frac{1}{31}-\frac{1}{37}\right)\)
\(L=\frac{1}{6}.\left(1-\frac{1}{37}\right)\)
\(L=\frac{1}{6}.\frac{36}{37}\)
\(L=\frac{6}{37}\)
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)
\(=5\left[\left(1-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{11}\right)+...+\left(\frac{1}{26}-\frac{1}{31}\right)\right]\)
\(=5\left[1-\frac{1}{31}\right]\)
\(=5.\frac{30}{31}=\frac{150}{31}\)
\(L=\frac{1}{7}+\frac{1}{91}+\frac{1}{247}+\frac{1}{775}+\frac{1}{1147}\)
\(L.6=\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+\frac{6}{19.25}+\frac{6}{25.31}\)
\(L.6=\left(1-\frac{1}{7}\right)+\left(\frac{1}{7}-\frac{1}{13}\right)+\left(\frac{1}{13}-\frac{1}{19}\right)+\left(\frac{1}{19}-\frac{1}{25}\right)+\left(\frac{1}{25}-\frac{1}{31}\right)\)
\(L.6=1-\frac{1}{31}\)
\(L.6=\frac{31}{31}-\frac{1}{31}\)
\(L.6=\frac{25}{31}\)
\(L=\frac{30}{31}:6\)
\(L=\frac{30}{31}.\frac{1}{6}\)
\(L=\frac{30}{186}\)
S=5*5/1*6 + 5*5/6*11+...+5*5/26*31
S=5*(5/1*6+5/6*11+...+5/26*31)
S=5*(1-1/6+1/6-1/11+...+1/26-1/31)
S=5*(1-1/31)
S=5*30/31
S=150/31
Vậy S=150/31
Tính tổng
a. 1/1.2 + 1/2.3 + 1/3.4 + ...+ 1/2015.2016
b. 2/1.3 + 2/3.5 + 2/5.7 + ...+ 2/99.101
c. 5/1.3 + 5/3.5 + 5/5.7 + ...+ 5/99.101
d. 1/2 + 1/6 + 1/12 + 1/20 + ...+ 1/9900
bn nào trả lời nhanh mik tích, cảm ơn ạ
còn cần không bạn, mk làm cho
a,1/1.2 + 1/2.3 + 1/ 3.4+....+ 1/2017.2018
b, 2/3.5+ 2/ 5.7 + 2/7.9 +....+ 2/.91.99
Ai giúp mink tích cho!
a) \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{2017\cdot2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}\)
\(=\frac{2017}{2018}\)
b) \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{97\cdot99}\)( sửa 91.99 thành 97.99 mới đúng nha )
\(=\frac{1}{2}\left(\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{97}-\frac{2}{99}\right)\)
\(=\frac{1}{2}\left(\frac{2}{3}-\frac{2}{99}\right)\)
\(=\frac{1}{2}.\frac{64}{99}\)
\(=\frac{32}{99}\)
a) 1/1.2 + 1/2.3 + 1/3.4 +...+1/2017.2018
= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ....+1/2017 - 1/2018
= 1 - 1/2018
= 2017/2018
Tính các tổng sau bằng phương pháp hợp lí nhất:
A= 1/1.2 + 1/2.3 + 1/3.4+...+ 1/49.50
B= 2/3.5 + 2/5.7 + 2/7.9+...+ 2/37.39
A=1/1-1/2+1/2-1/3+1/3-1/4+....+1/49-1/50
A=1/1-1/50
A=49/50
Vay A=49/50
B=1/3-1/5+1/5-1/7....+1/37-1/39
B=1/3-1/39
b=36/117
B=4/13
Tính giá trị của các biểu thúc sau:
a,-3/5+4/5+-1/5
b,-8/15+[-5/6+8/15]
c,[2/3+-3/4+5/12]:2/3+3/4
d,A=1/1.2+1/2.3+1/3.4+.....+1/49.50
e,2/3.5+2/5.7+2/7.9+.....+2/37.39
f,C=1/6.10+1/10.14+........+1/402.406
g,D=4/5.8+4/8.11+.......+4/305.308
Bài 1:Tính:
a,3 14/19 + 13/17 + 35/43 + 6 5/19 + 8/13
b,130 25/28 + 120 17/35
c,17 2/31 - (15/17 + 6 2/31)
d,(31 6/13 + 5 9/41) - 31 6/13
e,(17 24/31 - 3 7/8) - (2 38/31 - 4)
g,1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6
h,1/1.2 + 1/2.3 + 1/3.4 + .........+ 1/49.100
i,1/1.3 + 1/3.5 + 1/5.7 +........+ 1/97.99
1, Tính giá trị biểu thức
\(A=\frac{5}{1.2}+\frac{5}{2.3}+.......+\frac{5}{99.100}
\)
\(B=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
A = \(\frac{5}{1.2}\) + \(\frac{5}{2.3}\) +........+\(\frac{5}{99.100}\)
A = 5.(\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) +......+\(\frac{1}{99.100}\) )
A = 5. ( \(\frac{1}{1}\) - \(\frac{1}{2}\) +\(\frac{1}{2}-\frac{1}{3}\) +......+\(\frac{1}{99}-\frac{1}{100}\) )
A= 5. (\(1-\frac{1}{100}\))
A= 5.\(\frac{99}{100}\)
A= \(\frac{99}{20}\)
B = \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\)+............+ \(\frac{1}{9.10}\)
= \(\frac{1}{2}\)- \(\frac{1}{3}\)+\(\frac{1}{3}\)- \(\frac{1}{4}\)+ ...................+\(\frac{1}{9}\)- \(\frac{1}{10}\)
= \(\frac{1}{2}\) - \(\frac{1}{10}\)
= \(\frac{2}{5}\)
C = 2/3.5 + 2/5.7 + 2/7.9 + 2/9.11 + 2/11.13 + 2/13.15 = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15 =
= 1/3 - 1/15 = 5/15 - 1/15 = 4/15
1, Tính gái trị biểu thức
\(A=\frac{5}{1.2}+\frac{5}{2.3}+......+\frac{5}{99.100}\)
\(B=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(A=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{99.100}\)
\(A=5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(A=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=5\left(1-\frac{1}{100}\right)\)
\(A=5.\frac{99}{100}\)
\(A=\frac{99}{20}\)
\(B=\frac{1}{1.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(B=\frac{1}{2}-\frac{1}{10}\)
\(B=\frac{2}{5}\)
\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(C=\frac{1}{3}-\frac{1}{15}\)
\(C=\frac{4}{15}\)
\(A=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{99.100}\)
\(A=5\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(A=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=5\left(1-\frac{1}{100}\right)\)
\(A=5.\frac{99}{100}\)
\(A=\frac{99}{20}\)
\(B=\frac{1}{1.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(B=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(B=\frac{1}{2}-\frac{1}{10}\)
\(B=\frac{2}{5}\)
\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)
\(C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(C=\frac{1}{3}-\frac{1}{15}\)
\(C=\frac{4}{15}\)