Question

1 . tính nhanh

A = 1/2 + 1/6 + 1/12 + 1/20 + ............. 1/99.100

mk cần gấp giúp mk sẽ like cho mỗi ngày nếu đúng

( chú ý :/ :phần )

Answer 1

\(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{99.100}\)

\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{99.100}\)

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

\(A=\dfrac{1}{1}-\dfrac{1}{100}=1-\dfrac{1}{100}=\dfrac{99}{100}\)

Answer 2

Ta có:
\(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{9900}\)
\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)

Answer 3

Đề sai: 1/99.100