\(M=\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{19}{9^2.10^2}\)
\(M=\dfrac{2^2-1^2}{1^2.2^2}+\dfrac{3^2-2^2}{2^2.3^2}+\dfrac{4^2-3^2}{3^2.4^2}+...+\dfrac{10^2-9^2}{9^2.10^2}\)
\(M=1-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{9^2}-\dfrac{1}{10^2}\)
\(M=1-\dfrac{1}{10^2}< 1\left(đpcm\right)\)
Tính giá trị biểu thức:
B=\(\dfrac{5}{1\times2}+\dfrac{13}{2\times3}+\dfrac{25}{3\times4}+\dfrac{41}{4\times5}+...+\dfrac{181}{9\times10}\)
Chứng minh rằng :
\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{19}{9^2.10^2}< 1\)
Chứng minh rằng:
\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^3}+\dfrac{7}{3^2.4^2}+...+\dfrac{19}{9^2....10^2}< 1\)
Thực hiện phép tính
a, A = \(\left(\dfrac{1}{4\times9}+\dfrac{1}{9\times14}+\dfrac{1}{14\times19}+....+\dfrac{1}{44\times49}\right)\times\dfrac{1-3-5-7-....-49}{89}\)
b, B = \(\dfrac{2^{12}\times3^5-4^6\times9^2}{\left(2^2\times3\right)^6+8^4\times3^5}-\dfrac{5^{10}\times7^3-25^5\times49^2}{\left(125\times7\right)^3-5^9\times14^3}\)
Chứng minh rằng:
\(\dfrac{3}{1^2\cdot2^2}+\dfrac{5}{2^2\cdot3^2}+...........+\dfrac{19}{9^2\cdot10^2}< 1\)
cm:
\(\dfrac{3}{1^2.2^2}+\dfrac{7}{3^2.4^2}+\dfrac{11}{5^2.6^2}+\dfrac{15}{7^2.8^2}+\dfrac{19}{9^2.10^2}< 1\)
Cmr: \(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{19}{9^2.10^2}< 1\)
Giúp với ạ
CM:
\(\dfrac{3}{1^2.2^2}+\dfrac{7}{3^2.4^2}+\dfrac{11}{5^2.6^2}+\dfrac{15}{7^2.8^2}+\dfrac{19}{9^2.10^2}< 1\)
a) Tìm x biết: \(\dfrac{x+1}{100}+\dfrac{x+2}{99}=\dfrac{x+3}{98}+\dfrac{x+4}{97}\)
b) So sánh \(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{19}{9^2.10^2}\) với 1
c) Tìm GTNN của: A= |x-10|+|x-5|
