Cho A=\(\frac{1}{25}\)n và b=\(\frac{7}{6}\)+\(\frac{13}{12}\)\(\frac{21}{20}\)+....+\(\frac{2451}{2450}\)
Tìm n để A+B=49
Tìm x biết :
a) \(\frac{1}{2013}\times x+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2012\times2013}=2\)
b)\(2x+\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}+\frac{91}{90}=10\)
Tính nhanh:
a,\(\frac{7}{13}\cdot\frac{7}{15}-\frac{5}{12}\cdot\frac{21}{39}+\frac{49}{91}\cdot\frac{8}{15}\)
b,\(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right)\cdot\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
A=\(1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}+\frac{23}{132}-\frac{25}{156}\)\(\frac{25}{156}\)
Giups mình nha !!!
Đè thừa một số \(\frac{25}{156}\),mk ko lại đề bài nhé
\(A=1-\frac{2+3}{2\cdot3}+.....+\frac{11+12}{11\cdot12}-\frac{12+13}{12\cdot13}\)
\(=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-...+\frac{1}{11}+\frac{1}{12}-\frac{1}{12}-\frac{1}{13}\)
\(=\frac{1}{2}-\frac{1}{13}=\frac{11}{26}\)
1. Tính nhanh
a, \(\frac{7}{13}.\frac{7}{15}-\frac{5}{12}.\frac{21}{39}+\frac{49}{91}.\frac{8}{15}\)
b, \(\left(\frac{12}{199}+\frac{23}{200}-\frac{34}{201}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
c,\(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
Cho A=\(\frac{3}{2}+\frac{13}{12}+\frac{21}{20}+...+\frac{9901}{9900}\)và B=\(\frac{5}{6}+\frac{19}{20}+\frac{41}{42}+...+\frac{10099}{10100}\)Tính A-B
a) \(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
b)Cho \(A=\frac{n+2}{n-5}\left(n\inℤ;n\ne5\right)\). Tìm n để \(A\inℤ\)
c) Tìm \(x\inℕ\), biết:
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x.\left(x+1\right)}=\frac{6}{7}\)
a/ \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}=1-\frac{1}{10}\)
=> \(A=\frac{9}{10}\)
b/ \(A=\frac{n+2}{n-5}=\frac{n-5+7}{n-5}=\frac{n-5}{n-5}+\frac{7}{n-5}\)
=> \(A=1+\frac{7}{n-5}\)
Để A nguyên => 7 chia hết cho n-5 => n-5=(-7; -1; 1; 7)
=> n=(-2; 4, 6, 8)
1) tính:
a, ( \(\frac{17}{28}+\frac{18}{29}-\frac{19}{30}-\frac{20}{31}\) ).(\(\frac{-5}{12}+\frac{1}{4}+\frac{1}{6}\) )
b, \(\frac{\frac{7}{12}+\frac{5}{6}-1}{5-\frac{3}{4}+\frac{1}{3}}\)
2)Cho A=\(\frac{10n}{5n-3}\)
a) tìm n để A là số nguyên
b)tìm GTLN của A
Baif: A=\(\frac{10n}{5n-3}=2+\frac{6}{5n-3}\)
để A nguyên thì 5n-3 = Ư(6)={-1;-2;-3;-6;1;2;3;6}
xét từng TH:
5n-3=-1=>n=2/55n-3=-2=>n=1/55n-3=-3=>n=05n-3=-6=>n=-3/55n-3=1=>n=4/55n-3=2=>n=15n-3=3=>n=6/55n-3=6=>n=9/5b) A= \(\frac{10n}{5n-3}=2+\frac{6}{5n-3}\)
để A lớn nhất thì 5n-3 nhỏ nhất
1) tính:
a, (\(\frac{17}{28}+\frac{18}{29}-\frac{19}{30}-\frac{20}{31}\) ).(\(\frac{-5}{12}+\frac{1}{4}+\frac{1}{6}\) )
b, \(\frac{\frac{7}{12}+\frac{5}{6}-1}{5-\frac{3}{4}+\frac{1}{3}}\)
2)Cho A=\(\frac{10n}{5n-3}\)
a) tìm n để A là số nguyên
b)tìm GTLN của A
Rút Gọn:
a.\(\frac{36}{25}.\frac{85}{84}.\frac{20}{34}\)
b.\(\frac{7}{11}.\frac{-39}{190}.\frac{33}{13}.\frac{76}{21}\)
c.\(-\frac{11}{12}.\frac{4}{35}.\frac{84}{-25}.\frac{5}{6}\)
Bài làm
a) \(\frac{36}{25}.\frac{85}{84}.\frac{20}{34}\)
= \(\frac{36}{25}.\frac{85}{84}.\frac{10}{17}\)
= \(\frac{36.85.10}{25.84.17}\)
= \(\frac{12.17.2}{1.28.17}\)
= \(\frac{12.1.1}{1.14.1}\)
= \(\frac{6}{7}\)
~ Câu b,c làm tương tự thôi, không khó đâu, suy luận logic một chút là được mà ~
# Chúc bạn học tốt #
a) \(\frac{6}{7}\)
b)\(\frac{-6}{5}\)
c) \(\frac{22}{75}\)