(2 x X - 1)mũ 3 = (2 x X - 2)mũ 2

Bài này thầy Chung dạy rồi mà

\(\frac{1}{50\times51}+\frac{1}{51\times52}+...+\frac{1}{99\times100}\)

\(=\frac{51-50}{50\times51}+\frac{52-51}{51\times52}+...+\frac{100-99}{99\times100}\)

\(=\frac{1}{50}-\frac{1}{51}+\frac{1}{51}-\frac{1}{52}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{50}-\frac{1}{100}=\frac{1}{100}\)

Ta có \(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=\left(1+\dfrac{1}{3}+...+\dfrac{1}{99}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)=\left(1+\dfrac{1}{3}+...+\dfrac{1}{99}\right)+\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)-2.\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{100}\right)-\left(1+\dfrac{1}{2}+...+\dfrac{1}{50}\right)=\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}\)

\(\Rightarrow\text{Đ}PCM\)

B=1/50+1/51+1/52+...+1/99

Ta có: 1/50=1/50

          1/51<1/50

          1/52<1/50

          ..............

          1/99<1/50

1/50+1/51+1/52+...+1/99<1/50+1/50+1/50+...+1/50(50 phân số 1/50)

B<1

Ta ó: \(\frac{1}{50}>\frac{1}{100};\frac{1}{51}>\frac{1}{100};\frac{1}{52}>\frac{1}{100};....;\frac{1}{99}>\frac{1}{100}\)

\(\Rightarrow S>\frac{1}{100}+\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}\left(50so\right)=\frac{50}{100}=\frac{1}{2}\)

Vậy...

Ta có :

Tất cả các số hạng của tổng đều lớn hơn \(\frac{1}{100}\), mà tổng có 50 số hạng

=> S > \(\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}\)( có 50 số 1/100 )

=> S > \(\frac{50}{100}\)= \(\frac{1}{2}\)

Vậy S > 1/2

day ne