Question

Giúp mìn nhé cacq bạn

 

\(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{a.\left(a+1\right)}\\ Thanks\)

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Answer 1

\(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{a\left(a+1\right)}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{a}-\frac{1}{a+1}\)

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

Answer 2

\(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{a\left(a+1\right)}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{a}-\frac{1}{a+1}\)

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

Answer 3

Ta có:B=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+...+\(\frac{1}{a.\left(a-1\right)}\)

           B= \(\frac{2-1}{1.2}+\frac{3-2}{2.3}+...+\frac{a-\left(a-1\right)}{a.\left(a-1\right)}\)

           B= \(\frac{2}{1.2}-\frac{1}{1.2}+\frac{3}{2.3}-\frac{2}{2.3}+...+\frac{a}{a.\left(a-1\right)}-\frac{a-1}{a.\left(a-1\right)}\)

           B= 1-\(\frac{1}{2}\)+\(\frac{1}{2}-\frac{1}{3}+...+\frac{1}{a-1}-\frac{1}{a}\)

           B= 1-\(\frac{1}{a}\)

Vậy B=1-\(\frac{1}{a}\)

Chúc bạn học tốt! Cô giáo đã dạy mình thế đó!

Answer 4

\(B=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{a\left(a+1\right)}\)

\(\Rightarrow B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{a}-\frac{1}{a-1}\)

\(\Rightarrow B=1-\frac{1}{a+1}\)

\(\Rightarrow B=\frac{a}{a+1}\)

Vậy \(B=\frac{a}{a+1}\)