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Theo đề bài, ta có:
A = \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+...+\dfrac{6}{87.90}\)
A = \(2.\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+...+\dfrac{3}{87.90}\right)\)
A =\(2.\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
A = \(2.\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)= \(\dfrac{1}{8}\)
A= \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+...+\dfrac{6}{87.90}\)
A= \(2\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+...+\dfrac{3}{87.90}\right)\)
A= \(2\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
A= \(2\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)
A= 2. \(\dfrac{1}{16}\)
A= \(\dfrac{1}{8}\)
\(A=2\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+......+\frac{1}{87}-\frac{1}{90}\right)\)
\(\Rightarrow A=2\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(\Rightarrow A=2.\frac{1}{18}=\frac{1}{9}\)
\(A=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)
\(=6.\frac{1}{3}.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)
\(=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(=2.\frac{1}{18}\)
\(=\frac{1}{9}\)
\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{5.7}+...+\frac{2}{15.16}\)
\(=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(=2.\frac{3}{16}\)
\(=\frac{3}{8}\)
a) A = 1/3 - 1/7 + 1/7 - 1/11 +......+1/107 - 1/111
A = 1/3 - 1/111
A = ..............Bạn tự tính nhé!
b) B = 2.(3/15.18 + 3/18.21 +........+3/87.90)
B = 2.(1/15 - 1/18 + 1/18 - 1/21 +........+1/87 - 1/90)
B = 2.(1/15 - 1/90)
B = 2.5/90
B =......Tự tính nhé!
C ; D làm tương tự nhé!
\(B=\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+\frac{5}{24\cdot27}+...+\frac{5}{123\cdot126}\\ B=\frac{5}{3}\cdot\left(\frac{3}{18\cdot21}+\frac{3}{21\cdot24}+\frac{3}{24\cdot27}+...+\frac{3}{123\cdot126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{1}{18}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{7}{126}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\frac{1}{21}\\ B=\frac{5}{63}\)
Đây là những bài lớp 5+ vậy nên không làm theo kiểu lớp 5 được, cố gắng tìm bài đúng lớp nhé bạn (VNNLL cc)
A= 1/18 nhé bạn
xin lỗi vì mình không viết cách làm..........
\(\text{ta có:}\frac{6}{a\left(a+7\right)}+1=\frac{\left(a+1\right)\left(a+6\right)}{a\left(a+7\right)}\text{ do đó:}A=\frac{2.7}{1.8}.\frac{3.8}{2.9}.....\frac{101.106}{100.107}\)
\(=\frac{2.3...101.\left(7.8....106\right)}{1....101.\left(8.9.....107\right)}=\frac{7}{107}\)
đặt bt trên là A
\(\frac{1}{2}\)A=\(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\)
\(\frac{1}{2}\)A=\(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-....+\frac{1}{87}-\frac{1}{90}\)
\(\frac{1}{2}A=\frac{1}{15}-\frac{1}{90}\)
..... tự tính nhé