S= 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4 +...+ 1/50 - 1/50
S= 0 + 0 + 0 +...+ 0
S= 0
\(S=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{49.49}+\frac{1}{50.50}\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+...+\frac{1}{50}-\frac{1}{50}\)
\(=0+0+...+0\)
\(=0\)
So sánh A và 1 :
\(A=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{10.10}\)
\(\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{1010.1010}\)< 1. Chúng tỏ tổng này nhỏ hơn 1
Tính nhanh:
\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{2499}{2500}=\frac{1.3}{2.2}+\frac{2.4}{3.3}+\frac{3.5}{4.4}+...+\frac{49.51}{50.50}\)
Rồi phần sau ntn các bạn làm hộ mình với
Cho :A= \(\frac{1}{2.2}\) +\(\frac{1}{3.3}\) +\(\frac{1}{4.4}\)+....\(\frac{1}{1009.1009}\)
CMR A<\(\frac{3}{4}\)
Cho A= ( \(\frac{1}{2.2}\)-1).( \(\frac{1}{3.3}\)-1).( \(\frac{1}{4.4}\)-1)...( \(\frac{1}{100.100}\)-1)
So sánh A với -\(\frac{1}{2}\)
chung to :C = \(\frac{1}{1.1!}+\frac{1}{2.2!}+\frac{1}{3.3!}+...+\frac{1}{2019.2019!}< \frac{3}{2}\)
chứng tỏ \(\frac{1}{2.2}\) + \(\frac{1}{3.3}\) + .........+ \(\frac{1}{100.100}\) < 1
Giup mk tich cho
\(\frac{1}{2.2}\)+\(\frac{1}{3.3}\)+...........+\(\frac{1}{100.100}\)so sanh voi 1
Tính:
\(C=\) \(\frac{1.1!}{1!.2!}+\frac{2.2!}{2!.3!}+\frac{3.3!}{3!.4!}+......+\frac{100.100!}{100!.101!}\)
