Question

Chứng tỏ 1/n(n+1) = 1/n - 1/n+1

Tính

A=1/3.4 + 1/4.5 +...+ 1/9.10

Answer 1

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Answer 2

\(\frac{1}{n\left(n+1\right)}=\frac{\left(n+1\right)-n}{n\left(n+1\right)}=\frac{\left(n+1\right)}{n\left(n+1\right)}-\frac{n}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

\(\Rightarrow\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

Answer 3

a) 1/n.(n+1) = 1/n - 1/n+1 do

1/n - 1/ n+1 = n+1/n.(n+1)  -  n/n. (n+1) ( quy đồng mẫu)

                      = 1/ n .(n+1) (đpcm)

Answer 4

Có: VP=\(\frac{n+1-n}{n\left(n+1\right)}=\frac{1}{n\left(n+1\right)}=VT\)

A=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}=\frac{1}{3}-\frac{1}{10}=\frac{7}{30}\)

Answer 5

\(A=\frac{1}{3.4}+\frac{1}{4.5}+..+\frac{1}{9.10}\)

\(A=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)

\(A=\frac{1}{3}-\frac{1}{10}=\frac{7}{30}\)