Tính hợp lí
A=\(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{107.111}\)
Tính nhanh
A=\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{1}{107.111}\)
tính tổng sau : \(A=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)
Chứng minh rằng:
a,\(\frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+...+\frac{5}{\left(4n-1\right).\left(4n+3\right)}=\frac{5n}{3.\left(4n+3\right)}\)
b,\(\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+100}< \frac{1}{4}\)
\(\frac{1}{3.7}+\frac{1}{7.11}+.....+\frac{1}{\left(4x+3\right)\left(4x+7\right)}=\frac{5}{12}\)
cho S= \(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{2019.2023}.HãysosanhSvoi\frac{504}{6068}\)
Cho A = \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{103.107}\). So sánh A với 1
Cần gấp ạ
Câu 1 \(A=\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{107.111}\)
\(B=\frac{6}{15.18}+\frac{6}{18.21}+...+\frac{6}{87.90}\)
Câu 2
a) \(x+\frac{7}{12}=\frac{17}{18}-\frac{1}{9}\)
b) \(x+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}=\frac{-37}{45}\)
c)\(x-\frac{20}{11.13}-\frac{20}{13.15}-...-\frac{20}{53.55}=\frac{3}{11}\)
Chứng minh:
\(\frac{5}{3.7}+\frac{5}{7.11}+...+\frac{5}{\left(4n-1\right)\left(4n+3\right)}\)\(=\frac{5n}{4n+3}\)
