\(A=1+1+1+1-\left(\frac{1}{3}-\frac{1}{15}-\frac{1}{35}-\frac{1}{63}\right)\)
\(A=4+\left(\frac{1}{1.3}-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}\right)\)
\(A=4+\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)\)
\(A=4+\left(1-\frac{1}{9}\right)\)
\(A=4+\frac{8}{9}=\frac{44}{9}\)
Vậy A=44/9
Tìm x:
\(3x-\frac{1}{3}-\frac{1}{15}-\frac{1}{35}-\frac{1}{63}-\frac{1}{99}=0\)
\(A=\frac{1}{3}+\frac{13}{15}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}+\frac{141}{143}\)
1/ Tính:
a) \(\frac{1}{2}-2\left(\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+...+\frac{1}{48\cdot50}\right)\)
b) \(\frac{-1}{3}+\frac{-1}{15}+\frac{-1}{63}+...+\frac{-1}{9999}\)
c) \(\frac{8}{9}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-...-\frac{1}{6}-\frac{1}{2}\)
d) \(1-\frac{1}{2\cdot5}-\frac{1}{5\cdot8}-\frac{1}{8\cdot11}-...-\frac{1}{89\cdot92}-\frac{1}{92\cdot95}\)
2/ Tìm x:
\(3x-\frac{1}{3}-\frac{1}{15}-\frac{1}{35}-\frac{1}{63}-\frac{1}{99}=0\)
Tính \(\frac{-1}{3}\)+\(\frac{-1}{15}\)+\(\frac{-1}{35}\)+\(\frac{-1}{63}\)+........+\(\frac{-1}{9999}\)
Tính tổng
\(M=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)\left(\frac{1}{121}-1\right)\)
\(S=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{99}\)
\(Q=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2013.2015}\)
Tính nhanh :
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(D=\frac{1}{2}+\frac{-1}{5}+\frac{-5}{7}+\frac{1}{6}+\frac{-3}{35}+\frac{1}{3}+\frac{1}{41}\)
\(E=\frac{-1}{2}+\frac{3}{5}+\frac{-1}{9}+\frac{1}{127}+\frac{-7}{18}+\frac{4}{35}+\frac{2}{7}\)
\(A=\frac{1}{3}+\frac{13}{15}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}+\frac{141}{143}+\frac{193}{195}\)
Chứng tỏ rằng A không là số nguyên.
a)\(\frac{1}{1\cdot4}\)+\(\frac{1}{4\cdot7}\)+\(\frac{1}{7\cdot10}\)+. . .+\(\frac{1}{100\cdot103}\)
b)\(\frac{1}{2000\cdot1999}\)-\(\frac{1}{1999\cdot1998}\)-\(\frac{1}{1998\cdot1997}\)-. . .-\(\frac{1}{3\cdot2}\)-\(\frac{1}{2\cdot1}\)
c) \(\frac{-1}{3}\)+\(\frac{-1}{15}\)+\(\frac{-1}{35}\)+\(\frac{-1}{63}\)+. . .+\(\frac{-1}{9999}\)
Mong mọi người giúp đỡ
thực hiên các phép tính tính :
a) \(\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{1}{14}+\frac{1}{7}-\frac{-3}{35}\right).\frac{-4}{3}}\)
b) \(\frac{\left(1+2+3+...+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
