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bài A: áp dụng công thức: 1 + 2 + 3 + ... + n = n x (n + 1) : 2 tính được 5050
bài B: áp dụng công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\) rồi triệt tiêu gần hết, qui đồng mẫu số tính được B = 99/100
A = 1 + 2 + 3 + 4 + 5 + ... + 99 + 100
= ( 100 + 1 ) x 100 : 2 = 5050
Vậy A = 5050
\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Vậy \(B=\frac{99}{100}\)
Học tốt #
C=\(\frac{7}{3.4}\)-\(\frac{9}{4.5}\)+\(\frac{11}{5.6}\)+\(\frac{13}{6.7}\)+\(\frac{15}{7.8}\)-\(\frac{17}{8.9}\)+\(\frac{19}{9.10}\)
=\(\frac{1}{3}\)+\(\frac{1}{4}\)-\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)+\(\frac{1}{6}\)-\(\frac{1}{6}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)+\(\frac{1}{8}\)-\(\frac{1}{8}\)-\(\frac{1}{9}\)+\(\frac{1}{9}\)+\(\frac{1}{10}\)
=\(\frac{1}{3}\)+\(\frac{1}{10}\)=\(\frac{13}{30}\)
\(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{19.20}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{5}-\frac{1}{20}\)
\(=\frac{4}{20}-\frac{1}{20}=\frac{3}{20}\)
\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+\frac{2}{15.17}\)
\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{17}\)
\(A=1-\frac{1}{17}\)
\(A=\frac{16}{17}\)
\(B=\frac{4}{1.3}+\frac{4}{3.5}+...+\frac{4}{9.11}+\frac{4}{11.13}\)
\(B=\frac{4}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(B=\frac{4}{2}\left(1-\frac{1}{13}\right)\)
\(B=\frac{4}{2}\cdot\frac{12}{13}\)
\(B=\frac{24}{13}\)
=> A= \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}\)
=> A= \(\frac{1}{1}-\frac{1}{17}\)
=> A= \(\frac{16}{17}\)
\(\Rightarrow B=2.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{1}-\frac{1}{13}\right)\)
\(\Rightarrow B=2.\frac{12}{13}\)
\(\Rightarrow B=\frac{24}{13}\)
\(3+\frac{2}{5}-\frac{3}{4}\times\frac{4}{5}\)
\(=3+\frac{2}{5}+\frac{3}{5}\)
\(=3+1\)
\(=4\)
a, 6/9+5/7+1/3=2/3+5/7+1/3=5/7+1=12/7
b, 17/7+6/5-20/14=17/7+6/5-10/7=6/5+1=11/5
c,2/5x1/4+3/4x2/5=2/5x(1/4+3/4)=2/5x1=2/5
d, 6/11:4/6+5/11:2/3=6/11:2/3+5/11:2/3=(6/11+5/11):2/3=3/2
nha
\(A=\frac{4}{4.5}+\frac{4}{5.6}+\frac{4}{6.7}+...+\frac{4}{47.48}\)
\(A=4.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+......+\frac{1}{47.48}\right)\)
\(A=4.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+.....+\frac{1}{47}-\frac{1}{48}\right)\)
\(A=4.\left(\frac{1}{4}-\frac{1}{48}\right)\)
\(A=4.\frac{11}{48}\)
\(A=\frac{11}{12}\)