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Tính A
Số số hạng: (10 - 1,01) : 0,01 + 1 = 900 số
=> A = (1,01 + 10). 900 : 2 = 4954,5
Tính B:
\(\frac{1}{2}.B=\frac{1}{2}.2-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(\frac{1}{2}.B=1-\frac{2+3}{2.3}+\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}+\frac{9+10}{9.10}\)
\(\frac{1}{2}.B=1-\frac{2+3}{2.3}+\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}+\frac{9+10}{9.10}\)
\(\frac{1}{2}.B=1-\left(\frac{1}{3}+\frac{1}{2}\right)+\left(\frac{1}{4}+\frac{1}{3}\right)-\left(\frac{1}{5}+\frac{1}{4}\right)+\left(\frac{1}{6}+\frac{1}{5}\right)-\left(\frac{1}{7}+\frac{1}{6}\right)+\left(\frac{1}{8}+\frac{1}{7}\right)-\left(\frac{1}{9}+\frac{1}{8}\right)+\left(\frac{1}{10}+\frac{1}{9}\right)\)\(\frac{1}{2}.B=1-\frac{1}{3}-\frac{1}{2}+\frac{1}{4}+\frac{1}{3}-\frac{1}{5}-\frac{1}{4}+\frac{1}{6}+\frac{1}{5}-\frac{1}{7}-\frac{1}{6}+\frac{1}{8}+\frac{1}{7}-\frac{1}{9}-\frac{1}{8}+\frac{1}{10}+\frac{1}{9}\)
\(\frac{1}{2}.B=1-\frac{1}{2}+\frac{1}{10}=\frac{6}{10}\Rightarrow B=\frac{6}{5}\)
=> 2.A + \(\frac{455}{3}\).B = 2.4954,5 + \(\frac{455}{3}\). \(\frac{6}{5}\) = 9909 + 182 = 10091
A = 1,01 + 1,02 + 1,03 + ... + 9,98 + 9,99 + 10
Dãy trên các số hạng cách nhau 0,01 đơn vị
Số số hạng của dãy A là :
( 10 - 1,01 ) : 0,01 + 1 = 900 ( số )
Tổng các số hạng của dãy A là :
( 10 + 1,01 ) x 900 : 2 = 4954.5
đ/s......
a) \(\frac{1}{3}.\frac{-6}{13}.\frac{-9}{10}.\frac{-13}{36}\)
\(=\left(\frac{1}{3}.\frac{-9}{10}\right)\left(\frac{-6}{13}.\frac{-13}{36}\right)\)
\(=\frac{-3}{10}.\frac{1}{6}\)
\(=\frac{-1}{20}\)
b) \(\frac{-1}{3}.\frac{-15}{17}.\frac{34}{45}\)
\(=\frac{-1}{3}.\frac{-2}{3}\)
\(=\frac{2}{9}\)
c) \(\left(1-\frac{1}{5}\right)\left(\frac{-3}{10}+\frac{1}{5}\right)\)
\(=\frac{4}{5}.\frac{-1}{10}\)
\(=\frac{-2}{25}\)
d) \(A=\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}+\frac{2}{3}\)
\(=\frac{1}{3}\left(\frac{4}{5}+\frac{6}{5}\right)+\frac{2}{3}\)
\(=\frac{1}{3}.2+\frac{2}{3}\)
\(=\frac{2}{3}+\frac{2}{3}\)
\(=\frac{4}{3}\)
e) \(11\frac{1}{4}-\left(2\frac{5}{7}+5\frac{1}{4}\right)\)
\(=\left(11\frac{1}{4}-5\frac{1}{4}\right)-2\frac{5}{7}\)
\(=6-2\frac{5}{7}\)
\(=5\frac{7}{7}-2\frac{5}{7}\)
\(=3\frac{2}{7}\)
\(A=\frac{15.3^{11}+4.27^1}{9^7}\)
\(\Rightarrow A=\frac{3.5.3^{11}+4.3^{3^1}}{\left(3^2\right)^7}\)
\(\Rightarrow A=\frac{3^{12}.5+4.3^3}{3^{14}}\)
\(\Rightarrow A=\frac{3^3.\left(5.3^8+4.3^3\right)}{3^{14}}\)
\(\Rightarrow A=\frac{32805+4}{177147}\)
\(\Rightarrow A=\frac{32809}{177147}\)
\(a,\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right).\)
\(=\left(\dfrac{21}{60}+\dfrac{44}{60}-\dfrac{75}{60}\right):\left(\dfrac{99}{180}-\dfrac{104}{180}\right).\)
\(=\left(\dfrac{65}{60}-\dfrac{75}{60}\right):\left(-\dfrac{5}{180}\right).\)
\(=-\dfrac{10}{60}:\left(-\dfrac{5}{180}\right).\)
\(=-\dfrac{1}{6}:\left(-\dfrac{1}{36}\right).\)
\(=-\dfrac{1}{6}.\left(-36\right).\)
\(=\dfrac{-1.\left(-36\right)}{6}=\dfrac{36}{6}=6.\)
Vậy......
\(b,\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}.\)
\(=\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}.\)
\(=\dfrac{5}{8}:\dfrac{15}{16}.\)
\(=\dfrac{5}{8}.\dfrac{16}{15}=\dfrac{5.16}{8.15}=\dfrac{1.2}{1.3}=\dfrac{2}{3}.\)
Vậy......
c, (làm tương tự câu b).
~ Học tốt!!! ~
Câu b:
Cm : (36^36 - 9^10) ⋮ 45
A = 36^36 - 9^10
A = 9^36.4^36 - 9^10
A = 9^10.(9^26.4^36 - 1)
A = 9^10.[(9^2)^13.(4^2)^18 - 1]
A = 9^10.[\(\overline{..1}^{13}\).\(\overline{..6}^{18}\) -1]
A = 9^10.[\(\overline{..6}-\overline{..1}\)]
A = 9^10.\(\overline{..5}\)
A ⋮ 9; 5
9 = 3^2; 5 = 5
BCNN(9; 5) = 45
A ∈ B(45) hay A ⋮ 45 (đpcm)
mọi người thật là nhẫn tâm
chẳng ai giúp mk
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Loại bn bè vs mấy ng chỉ là giả tạo thôi
a) Đặt \(A=\frac{7^{15}}{1+7+7^2+...+7^{14}}\)
Đặt \(B=1+7+7^2+...+7^{14}\)
\(\Rightarrow7B=7+7^2+...+7^{15}\)
\(\Rightarrow7B-B=6B=7^{15}-1\)
\(\Rightarrow B=\frac{7^{15}-1}{6}\)
\(\Rightarrow A=\frac{7^{15}-1+1}{\frac{7^{15}-1}{6}}=\left(7^{15}-1\right).\frac{6}{7^{15}-1}+\frac{6}{7^{15}-1}=6+\frac{6}{7^{15}-1}\)
Tự làm tiếp nha
Ta có: \(A=\frac13+\frac16+\cdots+\frac{1}{45}\)
\(=\frac26+\frac{2}{12}+\cdots+\frac{2}{90}\)
\(=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{9\cdot10}\right)\)
\(=2\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac19-\frac{1}{10}\right)\)
\(=2\left(\frac12-\frac{1}{10}\right)=1-\frac{2}{10}=\frac{8}{10}=\frac45\)
Ta có: \(2B=\frac53-\frac76+\frac{9}{10}-\frac{11}{15}+\cdots+\frac{17}{36}-\frac{19}{45}\)
=>\(2B=2\left(\frac56-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\cdots+\frac{17}{72}-\frac{19}{90}\right)\)
=>\(B=\frac56-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\cdots+\frac{17}{72}-\frac{19}{90}\)
=>\(B=\frac12+\frac13-\frac13-\frac14+\cdots+\frac18+\frac19-\frac19-\frac{1}{10}\)
=>\(B=\frac12-\frac{1}{10}=\frac{4}{10}=\frac25\)
=>A>B
kh hiểu đng viết j
dạng quy luật: A =1/2