\(\frac{1}{2^2}n=\frac{1}{2^2}.\left(\frac{1}{2^2}+\frac{1}{2^4}+...+\frac{1}{2^{100}}\right)\)
\(\frac{1}{4}n=\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{102}}\)
\(n-\frac{1}{4}n=\frac{1}{2^2}-\frac{1}{2^{102}}\)
\(\frac{3}{4}n=\frac{1}{4}-\frac{1}{2^{102}}< \frac{1}{4}\)
\(n< \frac{1}{4}.\frac{3}{4}\) suy ra n>1/2
Bài 2. Chứng minh:
B= \(\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{100^2}< \frac{1}{2}\)
a,A=\(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)
b,B=\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{998\times999\times100}\)
c,C=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1\times98+2\times97+3\times96+...+98\times1}\)
A = \(\frac{1}{2^2}\) + \(\frac{1}{3^2}\) + \(\frac{1}{4^2}\) + ....+ \(\frac{1}{100^2}\) < 1
sắp xếp theo thứ tự tăng dần : \(\frac{1}{3};\frac{1}{5};\frac{-2}{15};\frac{1}{6};\frac{-2}{-5};\frac{-1}{10};\frac{4}{15}\)
bài 1 : thực hiện phép tính
1) \(\frac{2}{3}+\frac{3}{4}+\frac{-1}{6}\) 2) \(\frac{1}{2}-\frac{2}{5}+\frac{-7}{10}\)
Tìm A, biết:
A = \(\frac{1}{2}+\frac{3}{4}+\frac{5}{6}+\frac{7}{8}+...+\frac{99}{100}\)
Bài 1. Chứng minh:
A= \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}< 1\)
+) A = ( 1,11 + 0,19 - 2,6 ) : ( 2,06 + 0,54 ) - ( \(\frac{1}{2}\) + \(\frac{1}{3}\) ) : 2
+) Tìm x :
a, (1,16 - x ) . 2,25 / 10 \(\frac{5}{9}\) - 7\(\frac{1}{4}\) . 2\(\frac{2}{11}\) = 75%
b) x + 25% .x = -1,25
c) x - 75% x = \(\frac{1}{4}\)
+) Tính nhanh nếu có thể :
a) 1\(\frac{1}{2}\) - 3\(\frac{3}{4}\) b) -8\(\frac{1}{6}\) - 7\(\frac{3}{2}\) c) 0,15 - 4,8 + 1,3 d) ( 2\(\frac{1}{3}\) + 3,5 ) : (-4\(\frac{1}{6}\) + 3\(\frac{1}{7}\) ) + 7,5
e) 11\(\frac{1}{4}\) + (2\(\frac{5}{7}\) + 5\(\frac{1}{4}\) ) f) \(\frac{4}{9}\) : ( \(\frac{1}{-7}\) + 6\(\frac{5}{9}\) :(-\(\frac{1}{7}\))
Tính nhanh giá trị biểu thức sau:
a) \(-\frac{9}{10}\cdot\frac{5}{14}+\frac{1}{10}\cdot\left(-\frac{9}{2}\right)+\frac{1}{7}\cdot\left(-\frac{9}{10}\right)\)
b)\(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}+\frac{1}{11}\right)\cdot132\)
c)\(-\frac{2}{3}\cdot\left(\frac{8}{9}\cdot\frac{8}{13}-\frac{8}{27}\cdot\frac{3}{13}+\frac{4}{3}\cdot\frac{22}{39}\right)\)
