c: \(C=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}=\dfrac{100}{2}=50\)
d: \(D=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot..\cdot\dfrac{98}{99}=\dfrac{1}{99}\)
Tính :
\(B=\frac{7}{4}\left(\frac{33}{12}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)\)
\(C=\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{7}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
Tính nhanh:
A = 1/3 - 3/4 - ( - 3/5 ) + 1/72 - 2/9 - 1/36 + 1/15
B = 1/ 5 - 3/7 + 5/9 - 2/11 + 7/13 - 9/16 - 7/13 + 2/11 - 5/9 + 3/7 - 1/5
C = 1/100 - 1/100 . 99 - 1/99 . 98 - 1/98 . 97 - ... - 1/3 . 2 - 1/ 2 . 1
Chứng minh:
a. \(A=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{8}-\dfrac{1}{16}+\dfrac{1}{32}-\dfrac{1}{64}< \dfrac{1}{3}\)
b.\(B=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}< \dfrac{3}{16}\)
c. \(C=\dfrac{1}{41}+\dfrac{1}{42}+\dfrac{1}{43}+...+\dfrac{1}{79}+\dfrac{1}{80}>\dfrac{7}{12}\)
Tính
a) A= 1+5+5^2+5^3+.....+5^100
b)B= 1/2+(1/2)^2+(1/2)^3+(1/2)^4+....+(1/2)^99
c)C= (4^5.9^4-2.6^9)/2^10.3^8+6^8.20
8 Chứng minh rằng :
a) \(\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...+\dfrac{99}{100!}< 1\) ; b) \(\dfrac{1.2-1}{2!}+\dfrac{2.3-1}{3!}+\dfrac{3.4-1}{4!}+...+\dfrac{99.100}{100!}\)
c) \(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{49.50}=\dfrac{1}{26}+\dfrac{1}{27}+\dfrac{1}{28}+...+\dfrac{1}{50}\)
d) \(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}< \dfrac{1}{2}\)
a, x - 128 = ( 4\(\frac{20}{21}\) - 5 ) : ( \(\frac{4141}{4242}\) - 1 ) : ( \(\frac{636363}{646464}\) - 1)
b, A= \(\frac{-7}{4}\) . ( \(\frac{33}{12}\) + \(\frac{3333}{2020}\) + \(\frac{333333}{303030}\) + \(\frac{33333333}{42424242}\) )
a, (3-1/4+2/3)-(5+1/3-6/5)-(6-7/4+3/2)
b, 1/3-3/4+3/5+1/64-2/9-1/36+1/15
c, 0,5+1/3+0,4+5/7+1/6-4/35
d, 8/9-1/72-1/56-1/42-1/30-1/12-1/6-1/2
Tinh hop li
Nhanh nhe! Milk se tang 3 hinh anh than tuong bn muon.
1) ( -213) + 186 + ( - 14 ) + 217 + 54 + ( - 49 )
2 ) - 38 . ( 25 - 4 ) + 25 . ( -4 + 38 )
3) -39 . ( 5 - 99 ) + 99 . ( 10 - 39 )
4 ) 1+ 3-5-7+9+ 11 - ....- 397 - 399
5) 1+ 2 + 2^2 + ... + 2 ^ 100
6) 3^102 - 3 ^ 100 - 3 ^ 98 -...3 ^2 - 3 ^0
Bài 1: Tính B = 1 + 2 + 3 + ... + 98 + 99
Bài 2: Tính C = 1 + 3 + 5 + ... + 997 + 999
Bài 3. Tính D = 10 + 12 + 14 + ... + 994 + 996 + 998
