Question

tính tổng

S = 1/2.3 + 1/3.4 + 1/4.5 +...+ 1/99.100

 

Answer 1

\(S=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(S=\frac{1}{2}-\frac{1}{100}\)

\(S=\frac{49}{100}\)

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Answer 2

\(S=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(S=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(S=1\times\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(S=1\times\frac{49}{100}\)

\(S=\frac{49}{100}\)

Answer 3

Ta có: \(S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

=>\(S=\frac{1}{2}-\frac{1}{100}=\frac{50}{100}-\frac{1}{100}=\frac{50-1}{100}=\frac{49}{100}\)

Vậy \(S=\frac{49}{100}\)

Answer 4

S=2/2-3 + 2/3-4 + ... + 2/99-100

= 2. ( 1/2 -1/3 + 1/3 -1/4 + ... + 1/99 - 1/100 )

= 2. (1/2 - 1/100)

= 2. (50/100 - 1/100)

= 2. 49/100

= 98/100 = 49/50

=)

Answer 5

S=1/2.3+1/3.4+.....+1/99.100

S=1/2-1/3+1/3-1/4+.....+1/99-1/100

S=1/2-1/100

S=49/100