Tính nhanh:
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{37\cdot38\cdot39}\)
Giúp mk nhé, mk đang gấp, lời giải nũa nha các bn
Tính nhanh:
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{37\cdot38\cdot39}\)
Giúp mk nhé, mk đang gấp, lời giải nũa nha các bn
= \(\left(1+\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+...+\frac{1}{38}-\frac{1}{38}+\frac{1}{39}\right)\)
= 1 + \(1+\frac{1}{39}=\frac{40}{39}\)
chỗ " 1 + " phía trước là bỏ
ngay chỗ dấu bằng thứ hai
a)\(\frac{\left(3\cdot4\cdot2^{16}\right)^2}{11\cdot2^{13}\cdot4^{11}-16^9}\)
b\(\left(1\cdot2\cdot3....\cdot9-1\cdot2\cdot3.....\cdot8-1\cdot2\cdot3....7\cdot8^2\right)\)
c)1152-(374+1152)+(-65+374)
d)(10^2+11^2+12^2):(13^2+14^2)
\(\dfrac{16^3\cdot3^{10}+120\cdot6^9}{4^6\cdot3^{12}+6^{11}}\). Tính
rút gọn
\(\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}\) \(\frac{5^{11}\cdot7^{12}+5^{11}\cdot7^{11}}{5^{12}\cdot7^{12}+9\cdot5^{11}\cdot7^{11}}\) \(\frac{1998\cdot1990+3978}{1992\cdot1991-3984}\)
\(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=\frac{2.2}{3}=\frac{4}{3}\)
câu sau tương tự nhé
giải hộ mk cả hai câu còn lại đc ko ? Cảm ơn nha
bài 1
A =\(\frac{3^7\cdot17-3^9}{2^3\cdot3^5}\)
B=\(\frac{\left(3\cdot4\cdot2^{16}\right)^2}{11\cdot2^{13}\cdot4^{11}-16^9}\)
C =\(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
\(A=\frac{3^7\cdot17-3^9}{2^3\cdot3^5}=\frac{3^7\left(17-3^2\right)}{2^3\cdot3^5}=\frac{3^7\cdot2^3}{2^3\cdot3^5}=9\)
\(B=\frac{3^2\cdot4^2\cdot2^{32}}{11\cdot2^{13}\cdot4^{11}-16^9}=\frac{3^2\cdot2^{36}}{2^{35}\cdot11-2^{36}}=\frac{3^2\cdot2^{36}}{2^{35}\left(11-2\right)}=\frac{3^2\cdot2^{36}}{2^{35}\cdot3^2}=2\)
\(\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}=\frac{3^{29}\left(11-3\right)}{2^2\cdot3^{28}}=\frac{3^{29}\cdot8}{2^2\cdot3^{28}}=6\)
\(C=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-3^{30}}{4.3^{28}}=\frac{3^{29}\left(11-3\right)}{4.3^{28}}=\frac{3.8}{4}=6\)
so sánh m và n
m = \(\frac{2}{1\cdot2}\)+ \(\frac{2}{2\cdot3}\)+..........+\(\frac{2}{99\cdot100}\)
n = \(\frac{3}{1\cdot3}\)+ \(\frac{3}{3\cdot5}\)+..........+ \(\frac{3}{97\cdot99}\)
Rồi giải nhanh cho mk. trước 4 h nhé. giải cả bài để mk hiểu
\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{99\cdot100}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}\)
\(=\frac{100}{101}\)
\(m=\frac{100}{101}\)
\(2N=\frac{3}{1}-\frac{3}{3}+\frac{3}{3}-\frac{3}{5}+...+\frac{3}{97}-\frac{3}{99}\)
\(2N=3-\frac{1}{33}\)
\(2N=\frac{98}{33}\)
\(N=\frac{49}{33}\)
\(M< 1< N\)
\(\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
giúp mk zới nhá vế sau mk chịu òi
-------------------------------------------------------
= \(\frac{1}{6}--\frac{10}{3}\)[1/6 - (-10/3)]
= \(\frac{7}{2}=3,5\)
Không pải vế trước đó nữa cơ vế sau thì ai mà chả làm đc
Tính:
a/\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)
b/\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)
c/\(\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)
\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)
\(=\frac{3^{17}\cdot\left(3^4\right)^{11}}{\left(3^3\right)^{10}\cdot\left(3^2\right)^{15}}\)
\(=\frac{3^{17}\cdot3^{44}}{3^{30}\cdot3^{30}}\)
\(=\frac{3^{61}}{3^{60}}\)
\(=3\)
\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)
\(=\frac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot\left(2\cdot3\right)^3}\)
\(=\frac{3^4\cdot2^{11}}{2^8\cdot2^3\cdot3^3}\)
\(=\frac{3^4\cdot2^{11}}{2^{11}\cdot3^3}\)
\(=\frac{3^4}{3^3}\)
\(=3\)
\(\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)
\(=\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2\cdot\left(2^{10}\cdot3^{31}+2^{40}\cdot3^6\right)}\)
\(=\frac{1}{2}\)
