Tìm số nguyên bé nhất không phải là ước của \(1\cdot2\cdot3\cdot...\cdot21\cdot22\cdot23.\)
chung minh rang \(\frac{1\cdot3\cdot5\cdot\cdot\cdot39}{21\cdot22\cdot23\cdot\cdot\cdot40}=\frac{1}{2^{20}}\)
\(\frac{1\cdot3\cdot5\cdot...\cdot39}{21\cdot22\cdot23\cdot...\cdot40}\)=\(\frac{1}{2^{20}}\)
\(\frac{1.3.5....39}{21.22.23.....40}=\frac{\left(1.3.5.....39\right).\left(2.4.6.....40\right)}{\left(21.22.....40\right).\left(2.4.6.....40\right)}\)
\(=\frac{1.2.3.4.....40}{21.22.....40.\left(1.2.3.....40\right)2^{20}}\)
\(=\frac{1}{2^{20}}\)
Chứng minh:
\(\frac{1\cdot3\cdot5\cdot...\cdot39}{21\cdot22\cdot23\cdot...40}\)=\(\frac{1}{2^{20}}\)
Chứng minh rằng:
a)\(\frac{1\cdot3\cdot5\cdot\cdot\cdot39}{21\cdot22\cdot23\cdot\cdot\cdot40}=\frac{1}{2^{20}}\)
b)\(\frac{1\cdot3\cdot5\cdot\cdot\cdot\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\cdot\cdot\cdot2n}=\frac{1}{2^n}\)Với \(n\inℕ^∗\)
\(\frac{1414+1515+1616+1717+1818+1919}{20\cdot20+21\cdot21+22\cdot22+23\cdot23+24\cdot24+25\cdot25}\)Tính nhanh
Giải đầyđủ nha mình cần gấp lắm hôm nay phải có. Mơn nhìu <3
tính tổng sau:
\(A=1\cdot2\cdot3\cdot.....\cdot2021-1\cdot2\cdot3\cdot.....\cdot2021-1\cdot2\cdot3\cdot.....\cdot2019\cdot2020^2\)
\(A=1.2.3.4...2019.\left(2020.2021-2020^2\right)=1.2.3.4...2019.2020\)
chứng tỏ \(\frac{1}{1\cdot2}+\frac{1}{1\cdot2\cdot3}+\frac{1}{1\cdot2\cdot3\cdot4}+...+\frac{1}{1\cdot2\cdot3\cdot...\cdot100}< 1\)
N=\(\frac{5\cdot\left(2^2\cdot3^2\right)\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^6}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot2^{18}}\)
Tinh N
\(A=\frac{1\cdot2}{2\cdot2}\cdot\frac{2\cdot3}{3\cdot3}\cdot\frac{3\cdot4}{4\cdot4}\cdot\frac{4\cdot5}{5\cdot5}\cdot.................\cdot\frac{2012\cdot2013}{2013\cdot2013}\)với
\(B=\frac{2012\cdot2013-2012\cdot2012}{2012\cdot2011+2012\cdot2}\)
A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)
B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)
vậy A=B
\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}.\frac{4.5}{5.5}.....\frac{2012.2013}{2013.2013}=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2012}{2013}=\frac{1.2.3.4.5....2012}{2.3.4.5....2013}=\frac{1}{2013}\)
\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}=\frac{2012}{2012.2013}=\frac{1}{2013}\)
\(\Rightarrow A=B\)