Question

bài 1 chứng tỏ rằng

S=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+........+\(\frac{1}{49.50}\)< 1

S=\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+\(\frac{1}{4^2}\)+..........+\(\frac{1}{50^2}\)< 1

giúp mình với xin các bạn đó

mình tích cho

 

Answer 1

Mình còn chưa học lớp 6 huhu

Answer 2

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{49.50}< 1\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{49}-\frac{1}{50}< 1\)

\(S=1-\frac{1}{50}< 1\)

\(S=\frac{49}{50}< 1\left(đpcm\right)\)

Answer 3

\(S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{50^2}< \frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\)

\(S< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{50}-\frac{1}{51}\)

\(S< \frac{1}{2}-\frac{1}{51}\)

\(S< \frac{51}{102}-\frac{2}{102}\)

\(S< \frac{49}{102}< 1\left(đpcm\right)\)

Answer 4

\(S=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}< \frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{49.50}\)

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