Question

Cho A=\(\frac{1}{2}\)+\(\frac{1}{12}\)+\(\frac{1}{30}\)+...+\(\frac{1}{2450}\)và B=\(\frac{1}{26}\)+\(\frac{1}{27}\)+\(\frac{1}{28}\)+...+\(\frac{1}{50}\)

Tính A:B

 

 

Answer 1

A = 1/2 + 1/12 + 1/30 + ... + 1/2450

A = 1/1.2 + 1/3.4 + 1/5.6 + ... + 1/49.50

A = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/49 - 1/50

A = (1 + 1/3 + 1/5 + ... + 1/49) - (1/2 + 1/4 + 1/6 + ... + 1/50)

A = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/49 + 1/50) - 2.(1/2 + 1/4 + 1/6 + ... + 1/50)

A = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/49 + 1/50) - (1 + 1/2 + 1/3 + ... + 1/25)

A = 1/26 + 1/27 + 1/28 + ... + 1/50 = B

=> A:B = 1

Answer 2

\(A=\frac{1}{2}+\frac{1}{12}+\frac{1}{30}+....+\frac{1}{2450}\)

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}\)

\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)\)

\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{49}+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)\)

\(A=\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{49}+\frac{1}{50}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{25}\right)\)

\(A=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{49}+\frac{1}{50}=B\)

Vậy A = B

Answer 3

A = 1/2 + 1/12 + 1/30 + ... + 1/2450

A = 1/1.2 + 1/3.4 + 1/5.6 + ... + 1/49.50

A = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/49 - 1/50

A = (1 + 1/3 + 1/5 + ... + 1/49) - (1/2 + 1/4 + 1/6 + ... + 1/50)

A = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/49 + 1/50) - 2.(1/2 + 1/4 + 1/6 + ... + 1/50)

A = (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/49 + 1/50) - (1 + 1/2 + 1/3 + ... + 1/25)

A = 1/26 + 1/27 + 1/28 + ... + 1/50 = B

=> A:B = 1