4
\(A=\left(\frac{1}{\sqrt{25}+\frac{1}{5}+1}\right):\left(\frac{1}{25}-\frac{1}{\sqrt{25}-1}\right)..\)
\(B=\frac{1,5+0,\left(3\right)-0,1\left(6\right)}{2,5+1,\left(6\right)-0,8\left(3\right)}\)
\(C=1+7+7^2+.........+7^{50}\)
5
\(A=-\frac{1}{4}+\frac{7}{3}+\frac{3}{4}+\frac{9}{2}-\frac{5}{6}\)
\(B=\left(-0,75-\frac{1}{4}\right):\left(-5\right)+\frac{1}{15}-\left(-\frac{1}{5}:\left(-3\right)\right)\)
\(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+.....+\frac{1}{2015\cdot2016\cdot2017}\)
CÁC BN HÃY GIÚP EM 1 TÍ Ạ E KO NHỚ MẤY BÀI NÀY RA SAO Ạ
Em chỉ làm những bài e biết thôi, thông cảm nhs :D
a/ chịu
b/ \(C=1+7+7^2+.........+7^{50}\)
\(\Leftrightarrow7C=7+7^2+...........+7^{50}+7^{51}\)
\(\Leftrightarrow7C-C=\left(7+7^2+.......+7^{51}\right)-\left(1+7+.....+7^{50}\right)\)
\(\Leftrightarrow6C=7^{51}-1\)
\(\Leftrightarrow C=\dfrac{7^{51}-1}{6}\)
c/ \(A=\dfrac{-1}{4}+\dfrac{7}{3}+\dfrac{3}{4}+\dfrac{9}{2}\)
\(=\left(\dfrac{-1}{4}+\dfrac{3}{4}\right)+\left(\dfrac{7}{3}+\dfrac{9}{2}\right)\)
\(=\dfrac{1}{4}+\dfrac{41}{6}\)
\(=\dfrac{85}{12}\)
d/ Thấy phép tính hơi dài
e/ \(C=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+.........+\dfrac{1}{2015.2016.2017}\)
\(\Leftrightarrow2C=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+.........+\dfrac{2}{2015.2016.2017}\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+.......+\dfrac{1}{2015.2016}-\dfrac{1}{2016.2017}\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2016.2017}\)
\(=\dfrac{1}{2}-\dfrac{1}{4066272}\)
\(=\dfrac{2033136}{4066272}\)
\(\Leftrightarrow C=\dfrac{2033136}{4066272}:2\)
\(\Leftrightarrow C=?\)
