Question

Bài 1: Tính tổng S

S=1/1.4+1/4.7+1/7.10+1/10.13+1/13.16+1/16.19+1/19.22

Answer 1

Bài 1: Tính tổng S

\(S=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{19.22}\)

\(4S=\dfrac{4}{1.4}+\dfrac{4}{4.7}+\dfrac{4}{7.10}+...+\dfrac{4}{19.22}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{19}-\dfrac{1}{22}\)

\(=1-\dfrac{1}{22}\)

\(S=\dfrac{21}{22}.\dfrac{1}{4}=\dfrac{21}{88}\)

Answer 2

Ta có:
A  = 1/1.4 + 1/4.7 + 1/7.10 +...+ 1/16.19
3A= 1/3.(3/1.4 + 3/4.7 + 3/7.10 + ... + 3/16.19)
     = 1/3. (1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/16 - 1/19)
     = 1/3.(1 - 1/19)
     = 1/3. 18/19
    = 6/19