\(A=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+...+\frac{39}{19^2.20^2}\)
\(=1-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+...+\frac{1}{19^2}-\frac{1}{20^2}\)
\(=1-\frac{1}{20^2}\)
\(=\frac{399}{400}\)
Các câu hỏi tương tự
\(A=\frac{3}{1^2x2^2}+\frac{5}{2^2x3^2}+\frac{7}{3^2x4^2}+............+\frac{19}{9^2x10^2}\)
Chứng minh \(\frac{3}{1^2x2^2}+\frac{5}{2^2x3^2}+\frac{7}{3^2x4^2}+...+\frac{2013}{1006^2x1007^2}\) < 1
Tính:a) frac{left(1+frac{17}{1}right).left(1+frac{17}{2}right).left(1+frac{17}{3}right).....left(1+frac{17}{19}right)}{left(1+frac{19}{1}right).left(1+frac{19}{2}right).left(1+frac{19}{3}right).....left(1+frac{19}{17}right)}b) frac{frac{-6}{5}+frac{6}{19}-frac{6}{23}}{frac{9}{5}-frac{9}{19}+frac{9}{23}}c) frac{frac{1}{6}-frac{1}{39}+frac{1}{51}}{frac{1}{8}-frac{1}{52}+frac{1}{68}}d) frac{frac{2}{3}-frac{2}{5}-frac{2}{7}+frac{2}{11}}{frac{13}{3}-frac{13}{5}-frac{13}{7}+frac{13}{11}}e) frac{frac{1...
Đọc tiếp
Tính:
a) \(\frac{\left(1+\frac{17}{1}\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right).....\left(1+\frac{17}{19}\right)}{\left(1+\frac{19}{1}\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right).....\left(1+\frac{19}{17}\right)}\)
b) \(\frac{\frac{-6}{5}+\frac{6}{19}-\frac{6}{23}}{\frac{9}{5}-\frac{9}{19}+\frac{9}{23}}\)
c) \(\frac{\frac{1}{6}-\frac{1}{39}+\frac{1}{51}}{\frac{1}{8}-\frac{1}{52}+\frac{1}{68}}\)
d) \(\frac{\frac{2}{3}-\frac{2}{5}-\frac{2}{7}+\frac{2}{11}}{\frac{13}{3}-\frac{13}{5}-\frac{13}{7}+\frac{13}{11}}\)
e) \(\frac{\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2017}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}}\)
2) CMR: \(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{800}}< \frac{1}{3}\)
thực hiện phép tính (tính nhanh nếu có thể) :
a)\(1\frac{3}{19}+\frac{8}{21}-\frac{3}{19}+0.5+\frac{13}{21}\)
b)\(\left(-\frac{3}{4}+\frac{2}{7}\right):\frac{3}{7}+\left(\frac{5}{7}+\frac{-1}{4}\right):\frac{3}{7}\)
c)\(\left(\frac{1}{6}\right)^7\times6\)
d)\(\left(\frac{-1}{2}\right)^3+\frac{1}{2}:3\)
giúp mình với
1, tính
a, \(2^5+8\left[\left(-2\right)^3:\frac{1}{2}\right]^0-\left(\frac{1}{2}\right)^3\times2+\left(-2\right)^3\)
b, \(\frac{7}{15}-\frac{9}{19}-\frac{-8}{15}-\frac{10}{19}\)
c, \(1\frac{1}{3}:\frac{4}{5}+2\frac{2}{3}:\frac{4}{5}\)
1/Tính
a) \(\left(\frac{7}{2}+\frac{17}{3}\right).\frac{8}{19}-\left(\frac{5}{2}+\frac{14}{3}\right).\frac{8}{19}\)
b)\(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}\)
Tính \(A=\frac{8\frac{3}{9}.5\frac{1}{4}+3\frac{16}{19}.5\frac{1}{4}}{\left(2\frac{14}{17}-2\frac{1}{34}\right)34};\frac{7}{24}\)
Các bài toán Dạng CỘNG TRỪ LŨY THỪA CÙNG CƠ SỐ:
Bài 1: Tính:
A= \(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+........+\frac{1}{5^{19}}+\frac{1}{5^{20}}\) (RIÊNG BÀI 1 LÀM 2 CÁCH)
Bài 2: Chứng minh chia hết:
a, A= \(1-3+3^2-3^3+..........+3^{19}-3^{20}\)Chia hết cho 2
b, B= \(1+7+7^2+7^3+.........+7^{20}+7^{21}\) Chia hết cho 4
tính A= \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+....+\frac{19}{9^2.10^2}\)
giải hắn ra