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\(B=\frac{15.4^{12}.9^7-4.3^{15}.8^8}{19.2^{24}.3^{14}-6.4^{12}.27^5}=\frac{3}{1}=3\)
a) A = 110 - (-761) + 296 + 1454 - (-813 + 1077)
= 110 + 761 + 296 + 1454 - 264
= 871 + 1750 - 264
= 2631 - 264
= 2357
\(b=\text{}\dfrac{15.2^{24}.3^{14}-4.3^{15}.2^{24}}{19.2^{24}.3^{14}-6.2^{24}.3^{15}}=\)
\(=\dfrac{2^{24}.3^{14}\left(15-4.3\right)}{2^{24}.3^{14}\left(19-6.3\right)}=3\)
a) = 1/10 - 1/11 + 1/11 -1/12 + 1/12 - 1/13 +1/13 1/14 +...+ 1/78 - 1/79
= 1/10 - 1/79
= máy tính ok
mấy câu khác bn làm tương tự là đc nhưng nhớ nhanh thêm khoảng cách giữa các mẫu nha
a)\(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{78.79}=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{78}-\frac{1}{79}=\frac{1}{10}-\frac{1}{79}=\frac{69}{790}\)
b) \(\frac{8}{7.9}+\frac{8}{9.11}+...+\frac{8}{133.135}=4\left(\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{133.135}\right)\)
\(=4\left(\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{133}-\frac{1}{135}\right)=4\left(\frac{1}{7}-\frac{1}{135}\right)=4.\frac{128}{945}=\frac{456}{945}\)
c) \(\frac{12}{8.11}+\frac{12}{11.14}+...+\frac{12}{503.506}=4\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{503.506}\right)\)
\(=4\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{503}-\frac{1}{506}\right)=4\left(\frac{1}{8}-\frac{1}{506}\right)=\frac{249}{506}\)
d) \(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{391.394}=\frac{1}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{391.394}\right)\)
\(=\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{391}-\frac{1}{394}\right)=\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{394}\right)=\frac{1}{3}.\frac{195}{788}=\frac{65}{788}\)
e) \(\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{602.605}=\frac{4}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\right)\)
\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\right)=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{605}\right)=\frac{4}{3}.\frac{24}{121}=\frac{32}{121}\)
g) Sửa đề\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{820}=2\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1640}\right)=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{40.41}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{40}-\frac{1}{41}\right)=2\left(1-\frac{1}{41}\right)=2.\frac{40}{41}=\frac{80}{41}\)
\(=\frac{3.5.\left(2^2\right)^{12}.\left(3^2\right)^7-2^2.3^{15}.\left(2^3\right)^8}{19.2^{24}.3^{14}-2.3.\left(2^2\right)^{12}.\left(3^3\right)^5}\)
\(=\frac{3.5.2^{24}.3^{14}-2^2.3^{15}.2^{24}}{19.2^{24}.3^{14}-2.3.2^{24}.3^{15}}\)
\(=\frac{5.2^{24}.3^{15}-3^{15}.2^{26}}{19.2^{24}.3^{14}-2^{25}.3^{16}}\)
\(=\frac{2^{24}.3^{15}.\left(5-2^2\right)}{2^{24}.3^{14}.\left(19-3^2\right)}\)
\(=\frac{3.1}{10}\)
\(=\frac{3}{10}\)
rút gọn biểu thức nhé