Question

tính tổng 

1. A =1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2

chứng minh rằng A <2

2. S=3+3/2+3/2^2+3/2^4+...+3/2^9

Answer 1

A=\(\frac{1}{1^2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+...+\(\frac{1}{50^2}\)

A=1+\(\frac{1}{2^2}\)\(\frac{1}{3^2}\)+...+\(\frac{1}{50^2}\)

A<1+\(\frac{1}{1\cdot2}\)+\(\frac{1}{2\cdot3}\)+...+\(\frac{1}{49\cdot50}\)

A<1+1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+...+\(\frac{1}{49}\)-\(\frac{1}{50}\)

A<2-\(\frac{1}{50}\)<2

=>A<1(câu 1)

 

 

 

Answer 2

A= ^{\(\dfrac{1}{1^2}\)}