\(\frac{99}{98}-\frac{98}{97}-\frac{1}{97x98}\)

\(=\frac{99}{98}-\frac{98}{97}-\left(\frac{1}{97}-\frac{1}{98}\right)\)

\(=\frac{99}{98}-\frac{98}{97}-\frac{1}{97}+\frac{1}{98}=\left(\frac{99}{98}+\frac{1}{98}\right)+\left(-\frac{98}{97}-\frac{1}{97}\right)\)

\(=\frac{100}{98}-\frac{99}{97}=-\frac{1}{4753}\)

a) \(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}..1\frac{1}{99}=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}....\frac{100}{99}=\frac{2.2.3.3.4.4...10.10}{1.3.2.4.3.5...9.11}=\frac{\left(2.3.4...10\right)\left(2.3.4...10\right)}{\left(1.2.3...9\right)\left(3.4.5...11\right)}\)

\(\frac{10.2}{1.11}=\frac{20}{11}\)

b) \(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}\)

\(=\frac{1.3.2.4.3.5.4.6.5.7}{2.2.3.3.4.4.5.5.6.6}=\frac{\left(1.2.3.4.5\right).\left(3.4.5.6.7\right)}{\left(2.3.4.5.6\right).\left(2.3.4.5.6\right)}=\frac{1.7}{6.2}=\frac{7}{12}\)

c) \(\frac{99}{98}-\frac{98}{97}+\frac{1}{97.98}=\frac{99}{98}-\frac{98}{97}+\frac{1}{97}-\frac{1}{98}=\left(\frac{99}{98}-\frac{1}{98}\right)+\left(-\frac{98}{97}+\frac{1}{97}\right)=1-1=0\)

d) \(3\frac{1}{11}.\frac{27}{36}.1\frac{6}{7}.2\frac{4}{9}=\frac{34}{11}.\frac{3}{4}.\frac{13}{7}.\frac{22}{9}=\frac{34.3.13.22}{11.4.7.9}=\frac{34.13}{11.2.7.3}=\frac{442}{462}=\frac{221}{231}\)

Đặt \(A=\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{98}{2}+\frac{99}{1}\)

\(A=\left(\frac{1}{99}+1\right)+\left(\frac{2}{98}+1\right)+\left(\frac{3}{97}+1\right)+...+\left(\frac{98}{2}+1\right)+1\) ( 99/1 = 99, tất cả 98 ( không tính 99/1) hạng tử trong A đều cộng với 1 , dư ra 1 chỗ cuối)

\(A=\frac{100}{99}+\frac{100}{98}+\frac{100}{97}+...+\frac{100}{2}+\frac{100}{100}\) ( 100/100=1)

\(A=100.\left(\frac{1}{2}+...+\frac{1}{97}+\frac{1}{98}+\frac{1}{99}+\frac{1}{100}\right)\)

Thay A vào E, có:

\(E=\frac{100.\left(\frac{1}{2}+...+\frac{1}{97}+\frac{1}{98}+\frac{1}{99}+\frac{1}{100}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

\(E=100\)

\(\Rightarrow E=\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+....+\frac{98}{2}+1+1+...+1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)     ( Có 99 số 1)

\(\Rightarrow\frac{\frac{1}{99}+1+\frac{2}{98}+\frac{3}{97}+1+...+\frac{98}{2}+1+1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)(Nhóm 98 số 1 với 98 phân số đầu ở trên tử)mik viết thiếu nha sorry *-*

\(\Rightarrow E=\frac{\frac{100}{99}+\frac{100}{98}+\frac{100}{97}+...+\frac{100}{2}+\frac{100}{100}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

\(\Rightarrow E=\frac{\frac{100}{2}+\frac{100}{3}+\frac{100}{4}+...+\frac{100}{99}+\frac{100}{100}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

\(\Rightarrow E=\frac{100\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)

\(\Rightarrow E=\frac{100.1}{1}=100\)

~Chúc bạn hok tốt~

Trả lời :

\(E=100\)

ủng hộ nha !!!!

\(A=\frac{\frac{98}{2}+1+\frac{97}{3}+1+.....+\frac{2}{98}+1+\frac{1}{99}+1+1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+......+\frac{1}{99}+\frac{1}{100}}=\frac{\frac{100}{2}+\frac{100}{3}+........+\frac{100}{98}+\frac{100}{99}+\frac{100}{100}}{\frac{1}{2}+\frac{1}{3}+......+\frac{1}{99}+\frac{1}{100}}\)

    \(=\frac{100\left(\frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}\right)}{\left(\frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}\right)}=100\)

= 1 tk m nhé

bằng \(\frac{99}{98}\)

99/98

Phân tích mẫu ta có

99/1 + 98/2 +...+1/99 = (98/2 + 1) + (97/3 + 1) +...+(1/99 + 1) +99/1 - 99

( cộng 1 vào mỗi phân số trừ 99/1   do đó phải trừ đi 99 để vẵn được đẳng thức đó)

= 100/2 +100/3 +...+100/99 = 100. (1/2 +1/3 +...+1/99)

Do đó B = [100. (1/2 +1/3 +...+1/99)]/(1/2 +1/3 +..1/99) =100

Phân tích mẫu ta có

99/1 + 98/2 +...+1/99 = (98/2 + 1) + (97/3 + 1) +...+(1/99 + 1) +99/1 - 99

( cộng 1 vào mỗi phân số trừ 99/1   do đó phải trừ đi 99 để vẵn được đẳng thức đó)

= 100/2 +100/3 +...+100/99 = 100. (1/2 +1/3 +...+1/99)

Do đó B = [100. (1/2 +1/3 +...+1/99)]/(1/2 +1/3 +..1/99) =100

100 nhé

a= 7

b= 0

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