Ta có: \(\frac{1}{4}=\frac{1}{2\cdot2}< \frac{1}{1\cdot2}\)
\(\frac{1}{9}=\frac{1}{3\cdot3}< \frac{1}{2\cdot3}\)
\(\frac{1}{16}=\frac{1}{4\cdot4}< \frac{1}{3\cdot4}\)
.............................................................
\(\frac{1}{10000}=\frac{1}{100\cdot100}< \frac{1}{99\cdot100}\)
\(\Rightarrow\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{10000}< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}< 1\)
\(\Rightarrow\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{10000}< 1\)(đpcm)
Xin tk
Ta có: +++.....+=++.......+
mà ++.......+ < ++.......+
++.......+ < 1-+-+.......+-
++.......+ < 1-
++.......+ < 1
xl nhe em mình nó cứ vào copy phá nick của mình