\(C=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(C=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

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

\(C=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)

\(C=\frac{1}{100}-1+\frac{1}{100}\)

\(C=\frac{-49}{50}\)

C = 1/100 - 1/100.99 - 1/99.98 - 1/98.97 - ... - 1/3.2 - 1/2.1

C = 1/100 - (1/100.99 + 1/99.98 + 1/98.97 + ... + 1/3.2 + 1/2.1)

C = 1/100 - (1/1.2 + 1/2.3 + ... + 1/98.99 + 1/99.100)

C = 1/100 - (1 - 1/2 + 1/2 - 1/3 + ... + 1/98 - 1/99 + 1/99 - 1/100)

C = 1/100 - (1 - 1/100)

C = 1/100 - 99/100

C = -98/100 = -49/50

C = 1/100 - 1/100.99 - 1/99.98 - 1/98.97 - ... - 1/3.2 - 1/2.1

C = 1/100 - (1/100.99 + 1/99.98 + 1/98.97 + ... + 1/3.2 + 1/2.1)

C = 1/100 - (1/1.2 + 1/2.3 + ... + 1/97.98 + 1/98.99 + 1/99.100)

C = 1/100 - (1 - 1/2 + 1/2 - 1/3 + ... + 1/97 - 1/98 + 1/98 - 1/99 + 1/99 - 1/100)

C = 1/100 - ( 1 - 1/100)

C = 1/100 - 99/100

C = -98/100 = -49/50

1/100-1/100.99-1/99.98-1/98.97-...-1/3.2-1/2.1

=-(-1/100+1/100.99+1/99.98+1/98.97+...+1/3.2+1/2.1)

=-(-1/100+1/100-1/99+1/99-1/98+1/98-1/97+...+1/3-1/2+1/2-1)

=-(-1)=1

\(C=\frac{1}{100} -\left(\frac{1}{100.99}+\frac{1}{99.98}+...+\frac{1}{2.1}\right)=\frac{1}{100}-\left(1-\frac{1}{100}\right)=\frac{1}{100}-\frac{99}{100}=-\frac{49}{50}\)

chắc là 200,đoán thế thôi,chưa tính

Ta có:

\(A=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-\frac{1}{98.97}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

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

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

\(=\frac{1}{100}+\frac{1}{100}-1\)

\(=\frac{1}{50}-\frac{50}{50}\)

\(=-\frac{49}{50}\)

Câu này khó quá ta mình suy nghĩ này giờ mà vẫn chưa ra

\(C=\frac{1}{100}-\left(\frac{1}{100.99}+\frac{1}{99.98}+\frac{1}{98.97}+..+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

Đặt biểu thức trong ngoặc đơn là B ta có

\(B=\frac{100-99}{100.99}+\frac{99-98}{99.98}+\frac{98-97}{98.97}+...+\frac{3-2}{3.2}+\frac{2-1}{2.1}\)

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

\(B=1-\frac{1}{100}=\frac{99}{100}\)

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

\(C=\frac{1}{100}-\frac{1}{100.99}-\frac{1}{99.98}-...-\frac{1}{2.1}\)

\(\Rightarrow C=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(\Rightarrow C=\frac{1}{100}-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(\Rightarrow C=\frac{1}{100}-\left(1-\frac{1}{100}\right)\)

\(\Rightarrow C=\frac{1}{100}-1+\frac{1}{100}\)

\(\Rightarrow C=\frac{1}{50}-1\)

\(\Rightarrow50C=\left(\frac{1}{50}-1\right)50\)

\(\Rightarrow50C=1-50\)

\(\Rightarrow50C=-49\)

Vậy \(50C=-49\)

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