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\(D=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot......\cdot\frac{99}{100}\) chứng minh rằng \(D< \frac{1}{10}\)
Cho M=\(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot....\cdot\frac{99}{100}\)
N=\(\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot......\cdot\frac{100}{101}\)
a, Tính M\(\times\)N
b, CM M<\(\frac{1}{10}\)
So sánh M và N, biết
\(M=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)và \(N=\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{100}{101}\)
cho A=\(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\cdot\cdot\frac{99}{100}\)
CHỨNG MINH \(\frac{1}{15}< a< \frac{1}{10}\)
CHO A = \(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot\cdot\cdot\frac{99}{100}\)
CHỨNG MINH \(\frac{1}{15}< A< \frac{1}{10}\)
27 tháng 2 2017 lúc 20:29
Cho A = \(\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)
Chứng minh rằng \(\frac{1}{15}< A< \frac{1}{10}\)
a) left(frac{11}{4}cdotfrac{-5}{9}-frac{4}{9}cdotfrac{11}{4}right)cdotfrac{8}{33}b) frac{-1}{4}cdotfrac{152}{11}+frac{68}{4}cdotfrac{-1}{11}c) frac{-2}{3}cdotfrac{4}{5}+frac{2}{3}cdotfrac{3}{5}d) left(frac{1}{2}-1right)cdotleft(frac{1}{3}-1right)cdotleft(frac{1}{4}-1right)cdot....cdotleft(frac{1}{100}-1right)e) frac{3}{2^2}cdotfrac{8}{3^2}cdotfrac{15}{4^2}cdot...cdotfrac{8^{99}}{30^2}
Đọc tiếp
a) \(\left(\frac{11}{4}\cdot\frac{-5}{9}-\frac{4}{9}\cdot\frac{11}{4}\right)\cdot\frac{8}{33}\)
b) \(\frac{-1}{4}\cdot\frac{152}{11}+\frac{68}{4}\cdot\frac{-1}{11}\)
c) \(\frac{-2}{3}\cdot\frac{4}{5}+\frac{2}{3}\cdot\frac{3}{5}\)
d) \(\left(\frac{1}{2}-1\right)\cdot\left(\frac{1}{3}-1\right)\cdot\left(\frac{1}{4}-1\right)\cdot....\cdot\left(\frac{1}{100}-1\right)\)
e) \(\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{8^{99}}{30^2}\)
Bài 19, Cho Afrac{1}{2}cdotfrac{3}{4}cdotfrac{5}{6}cdot...cdotfrac{99}{100} Bfrac{1}{10}So sánh A và B Bài 20, Cho Afrac{1}{2}cdotfrac{3}{4}cdotfrac{5}{6}cdot...cdotfrac{999}{1000} Bfrac{1}{100}So sánh A và BBài 21, Cho Afrac{1}{2}cdotfrac{3}{4}cdotfrac{5}{6}cdot...cdotfrac{2499}{2500} Chứng minh Afrac{1}{49}Bài 20, Cho Afrac{1}{2}cdotfrac{3}{4}cdotfrac{5}{6}cdot...cdotfrac{99}{100} Bfrac{2}{3}cdotfrac{4}{5}cdotfrac{6}{7}cdot...cdotfrac{10...
Đọc tiếp
Bài 19, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)
\(B=\frac{1}{10}\)
So sánh A và B
Bài 20, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{999}{1000}\)
\(B=\frac{1}{100}\)
So sánh A và B
Bài 21, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{2499}{2500}\)
Chứng minh A<\(\frac{1}{49}\)
Bài 20, Cho \(A=\frac{1}{2}\cdot\frac{3}{4}\cdot\frac{5}{6}\cdot...\cdot\frac{99}{100}\)
\(B=\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{100}{101}\)
\(C=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{6}{7}\cdot...\cdot\frac{98}{99}\)
1/ So sánh A, B, C
2/Chứng minh \(A\cdot C< A^2< \frac{1}{10}\)
3/Chứng minh \(\frac{1}{15}< A< \frac{1}{10}\)
tính nhanh a, frac{-2}{5}cdotleft(frac{5}{17}-frac{9}{15}right)-frac{2}{5}cdotfrac{2}{17}+frac{-2}{5}b, frac{1}{5}cdotleft(frac{4}{13}-frac{9}{11}right)+frac{1}{3}left(frac{9}{13}-frac{4}{22}right)c, left(frac{1}{2}+1right)cdotleft(frac{1}{3}+1right)cdotleft(frac{1}{4}+1right)cdot...cdotleft(frac{1}{99}+1right)d, left(1-frac{1}{2}right)cdotleft(1-frac{1}{3}right)cdotleft(1-frac{1}{4}right)cdot...cdotleft(1-frac{1}{100}right)
Đọc tiếp
tính nhanh
a, \(\frac{-2}{5}\cdot\left(\frac{5}{17}-\frac{9}{15}\right)-\frac{2}{5}\cdot\frac{2}{17}+\frac{-2}{5}\)
b, \(\frac{1}{5}\cdot\left(\frac{4}{13}-\frac{9}{11}\right)+\frac{1}{3}\left(\frac{9}{13}-\frac{4}{22}\right)\)
c, \(\left(\frac{1}{2}+1\right)\cdot\left(\frac{1}{3}+1\right)\cdot\left(\frac{1}{4}+1\right)\cdot...\cdot\left(\frac{1}{99}+1\right)\)
d, \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)