Question

[Ha viet hoa]

cho hai số A = 3/2+7/6+13/12+...+10101/10100 và B = 101 so sánh 2 số

Answer 1

[T.Anh 2K7(siêu quậy)(тoáɴ๖ۣۜнọc)]

Ta có\(A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+...+\left(1-\frac{1}{10100}\right)\)

\(A=\left(1+1+1+...+1\right)+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{10100}\right)\)

\(A=\left(1+1+1+...+1\right)+\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{100\times101}\right)\)

           100 số 1

\(A=100+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{100}-\frac{1}{101}\right)\)

\(A=100+\left(1-\frac{1}{101}\right)\)

\(A=100+1-\frac{1}{101}\)

\(A=101-\frac{1}{101}< 101=B\)

\(\Rightarrow A< B\)

Vậy A<B

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