Tính nhanh:
\(\frac{1}{20.21}+\frac{1}{21.22}+\frac{1}{22.23}+........+\frac{1}{60.61};\)
\(\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+........+\frac{4}{45.49}\)
Những câu hỏi liên quan
1. Giải phương trình
\(12-10,34.\frac{3}{13}\left(x-1\right)=\left(\frac{1}{21.22}+\frac{1}{22.23}+...+\frac{1}{29.30}\right).280\)
HELP ME!
\(12-10,34.\frac{3}{13}\left(x-1\right)=\left(\frac{1}{21.22}+\frac{1}{22.23}+...+\frac{1}{29.30}\right)280\)
<=> \(12-10,34.\frac{3}{13}\left(x-1\right)=\left(\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+...+\frac{1}{29}-\frac{1}{30}\right).280\)
<=> \(12-10,34.\frac{3}{13}\left(x-1\right)=\left(\frac{1}{21}-\frac{1}{30}\right)280\)
<=> \(12-10,34.\frac{3}{13}\left(x-1\right)=4\)
<=> \(8=10,34.\frac{3}{13}.\left(x-1\right)\)
<=> \(x-1=\frac{5200}{1551}\)
<=> \(x=\frac{6751}{1551}\)
Ta có:
\(\frac{1}{21.22}+\frac{1}{22.23}+...+\frac{1}{29.30}=\frac{1}{21}-\frac{1}{22}+\frac{1}{22}-\frac{1}{23}+...+\frac{1}{29}-\frac{1}{30}=\frac{1}{21}-\frac{1}{30}\)
phương trình đã cho trở thành
\(12-10,34.\frac{3}{13}\left(x-1\right)=\left(\frac{1}{21}-\frac{1}{30}\right).280\)
\(\Leftrightarrow x-1=\frac{\left(\frac{1}{21}-\frac{1}{30}\right).280-12}{-10,34.\frac{3}{13}}\Leftrightarrow x=\frac{\left(\frac{1}{21}-\frac{1}{30}\right).280-12}{-10,34.\frac{3}{13}}+1\)
\(\Leftrightarrow x=\frac{6751}{1551}\)
tính tổng 20.21+21.22+22.23+...+39.40
Ta có: \(S=20.21+21.22+22.23+....+39.40\)
\(\Rightarrow3S=3.20.21+3.21.22+.....+3.39.40\)
\(\Rightarrow3S=20.21.\left(22-19\right)+22.23.\left(24-21\right)+.....+39.40.\left(41-38\right)\)
\(\Rightarrow3S=39.40.41-19.20.21\)
\(\Rightarrow3S=55980\)
\(\Rightarrow S=18660\)
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Cách giải
=(39.40-20.21):0.01+1
=19.19:0.01+1
=1919+1
=1920
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3s=20.21.(22-19)+21.22.(23-20)+22.23.(24-21)+...+39.40.(41-38)
=20.21.22 - 20.21.19+21.22.23 - 21.22.20 +22.23.24 -22.23.21 + ...+ 39.40.41-39.40.38
=39.40.41- 20.21.19=63960-7980=55980
s=18660
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Tính giá trị biểu thức:
\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{21.22}\)
(TRÌNH BÀY CÁCH TÍNH RÕ RÀNG)
Đặt \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{21.22}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{21}-\frac{1}{22}\)
\(A=\frac{1}{5}-\frac{1}{22}\)
\(A=\frac{17}{110}\)
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\(\frac{1}{5.6}\)+\(\frac{1}{6.7}\)+...+\(\frac{1}{21.22}\)
=\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)+...+\(\frac{1}{21}\)-\(\frac{1}{22}\)
=\(\frac{1}{5}\)-\(\frac{1}{22}\)
=\(\frac{17}{110}\)
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\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{21}-\frac{1}{22}\)
\(A=\frac{1}{5}-\frac{1}{22}\)
\(A=\frac{22}{110}-\frac{5}{110}\)
\(A=\frac{17}{110}\)
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Tinh tong bang coach hop li nhat
S=20.21+21.22+22.23+...+39.40
Ai giai duoc Minh tich cho
TÌm x: ( 1.2.3 + 2.3.4 + ... + 20.21.22 ) - 5 - 7 - 9 - ... - 55 - 3x = \(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\right)-\frac{5}{1.3}-\frac{5}{3.5}-...-\frac{5}{53.55}-\) 8.9 - 9.10 - ... - 20.21
so sánh \(U=\frac{1.3.5.7...39}{21.22....40}\)và \(V=\frac{1}{2^{20}-1}\)
Biết:\(A=a+23.5+x.3-2.234+\frac{y}{2}+22.23+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\right)-23=29.171\)
Tìm \(A,a,x,y?\)
tính:
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{20.21}\)
giúp mik nha,ai làm nhanh và rõ ràng chinh xác thì mik sẽ k 3 cái luôn nha!!
\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{20.21}\)
\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{20.21}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{20}-\frac{1}{21}\right)\)
\(=2\left(1-\frac{1}{21}\right)=2.\frac{20}{21}=\frac{40}{21}\)
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=2.(1-1/2+1/2-1/3+1/3-1/4+...+1/20-1/21)
=2.(1-1/21)
=2.20/21
=40/21
k mik nha
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Xem thêm câu trả lời
So sánh P và Q :
P=\(\frac{1.3.5.....39}{21.22.....40}\) Q=\(\frac{1}{2^{20}-1}\)
