(1-\(\dfrac{1}{2}\)) . (1-\(\dfrac{1}{3}\)) . (1-\(\dfrac{1}{4}\)) ......... (1-\(\dfrac{1}{99}\)) = \(\dfrac{1}{2}\) .\(\dfrac{2}{3}\) . \(\dfrac{3}{4}\) ......... \(\dfrac{98}{99}\) = \(\dfrac{1}{99}\)
1. 1+ (-2) + 3+ (-4) + . . . +19 + (-20)
2. 1 - 2 + 3- 4 + . . . + 99 - 100
3. -1 + 3 -5 + 7 - . . . +97 - 99
4. 1+ 2 - 3+ 4 + . . . +97 + 98 - 99 - 100
a ) A = 1/4 + 1/4^2 +1/4^3 +.........+ 1/4^100 + 1/3.4^100
b) B = 1/3 - 1/3^2 + 1/3^3 - 1/3^4 +.........+ 1/ 3^99
Tính P=(1-1/2)(1-1/3)(1-1/4)...(1-1/99)
chứng minh rằng
1+1/3+1/5+1/7+...+1/99-(1/2+1/4+1/6+...+1/100)=1/51+1/52+...+1/100
Tính tích P = ( 1- 1/2). (1- 1/3). (1- 1/4) ... ( 1 -1/99)
Chứng tỏ rằng : 1/101 +1/102+ ... +1/299 + 1/300 > 2/3
Tính \(H=\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+...........+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+.............+\dfrac{1}{100}}:\dfrac{92-\dfrac{1}{9}-\dfrac{1}{10}-..............\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+........+\dfrac{1}{500}}\)
Help me!!!
tính
a; A = 3/4 * 8/9 * 15/16 * ..............* 9999/10000
b; B = {1 - 1/21 } * { 1 - 1/28 } * {1 - 1/36 } * .......................*{ 1 - 1326}
c; C = { 1 + 1/1*3 } * { 1 + 1 / 2*4 } * { 1 + 1/3*5} * ...........................* { 1+ 1/99*101}
Cho A= 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/99 + 1/100. Chứng tỏ 7/12 < A <5/6
Tính H=1/99+1/98+3/97+...+98/2+99/1/1/2+1/3+1/4+...+1/100:92-1/9-2/10-3/11-...-92/100/1/45+1/50+1/55+...+1/500.
Mong các bạn hiểu và giúp mình nha.