CHO MÌNH HỎI:
CHO K = (1/2^2-1)*(1/3^2-1)*(1/4^2-1)*...*(1/100^2-1). SO SÁNH K VỚI -1/2
Giúp mình giải bài này với!
Cho K=\(\left\{\frac{1}{2^2}-1\right\}\times\left\{\frac{1}{3^2}-1\right\}\times\left\{\frac{1}{4^2}-1\right\}\times...\times\left\{\frac{1}{100^2}-1\right\}\)
So sánh K với \(\frac{-1}{2}\)
\(K=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}...\frac{-9999}{10000}=\left(-1\right)^{99}.\frac{1.3.2.4...99.101}{2.2.3.3.4.4...100.100}=-\frac{1.2...99}{2.3...100}.\frac{3.4...101}{2.3...100}=-\frac{1}{100}.\frac{101}{2}=-\frac{101}{200}< -\frac{100}{200}=-\frac{1}{2}\)
cho \(K=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right)...\left(\frac{1}{100^2}-1\right)\). So sánh K với\(\frac{-1}{2}\)
cho k=(\(\frac{1}{2^2}\)-1)(\(\frac{1}{3^2}\)-1)...(\(\frac{1}{100^2}\)-1).so sánh k với \(\frac{-1}{2}\)
K= 1/2 x 3/4 x5/6 x.........x97/98 x99/100
So sánh K với 1/15
k tính hãy so sánh
a,23-(-17).(-39).(-148) với 23
b,1 .(-2).(-3).(-4)......(-99).(-100) với (-1).(-2).(-3).(-4).....(-100).(-101)
Cho A= (1/2^2-1).(1/3^2-1).(1/4^2-1).............(1/100^2-1). So sánh A với -1/2
nhanh mỗi ngày mình tích 3 cái
Nhờ các bạn giải hộ mình toán lớp 5.Xin cám ơn.
K = 1/2 + 3/4 + 5/6 + ............97/98 + 99/100
So sánh K với 1/15.
A=1/2^2+1/4^2+1/6^2+...+1/14^2 hãy so sánh với 1/2
3 k
Ta co:\(A=\frac{1}{2.2}+\frac{1}{4.4}+\frac{1}{6.6}+...+\frac{1}{14.14}< \frac{2}{2.4}+\frac{2}{4.6}+\frac{1}{6.8}+...+\frac{2}{14.16}\left(1\right)\)
\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{14.16}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{16}\)
\(=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}< \frac{8}{16}=\frac{1}{2}\left(2\right)\)
\(\left(1\right),\left(2\right)\Rightarrow A< \frac{1}{2}\)
V...
cho dong dau tien la dau =,chu ko phai dau < nhe
1)Tính tổng:a)3+3/5+3/25+3/125+3/625
b)M=4/3.7+4/7.11+4/11.15+...+8/95.99
c)N=1/2+1/6+1/12+1/20+...+1/90
2)Cho K=1+1/3+1/1/6+1/10+...+1/45 so sánh K với 2
Ta có ; K = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{45}\)
\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{90}\)
\(=1+\left(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+.....+\frac{2}{9.10}\right)\)
\(=1+2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}\right)\)
\(=1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=1+2\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=1+1-\frac{1}{5}\)(nhân phá ngoặc)
\(=2-\frac{1}{5}\)< 2
Vậy K = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{45}\)< 2