\(1\cdot99+2\cdot98+3\cdot97+...+50\cdot50\)
\(=1\left(100-1\right)+2\left(100-2\right)+...+50\left(100-50\right)\)
\(=100\left(1+2+...+50\right)-\left(1^2+2^2+...+50^2\right)\)
\(=100\cdot\dfrac{50\cdot51}{2}-\dfrac{50\left(50+1\right)\left(2\cdot50+1\right)}{6}\)
\(=100\cdot25\cdot51-\dfrac{50\cdot51\cdot101}{6}\)
\(=2500\cdot51-425\cdot101\)
=127500-42925
=84575
1/2+1/12+1/30+...+1/9120+1/9506+1/9900. / 50-50/51-51/52-...-97/98-98/99-99/100
Tìm x , y, z biết
\(\frac{x+99}{-1}=\frac{y-98}{2}=\frac{z+97}{-3}\)và x-y+z=50
Rút gọn các biểu thức sau:
a) \(1+5+5^2+5^3+5^4+...+5^{50}\)
b) \(3^{99}-3^{98}-3^{97}-...-3-1\)
Tính :
a. B= 2100 - 299 + 298 - 297 + ... + 22
b. C= (1000-13).(1000-23).(1000-33)...(1000-503)
Tính :
a. B= 2100 - 299 + 298 - 297 + ... + 22
b. C= (1000-13).(1000-23).(1000-33)...(1000-503)
A) Tính M: 3/4.8/9.15/16.9999/10000 B) Chứng tỏ rằng: 1/26+1/27+...+1/50=99/50-97/49+...+7/4-5/3+3/2-1
cho T = 1/2 + 1/3 + 1/4 +....+ 1/99 + 1/100 và M = 1/99 + 2/98 + 3/97 + ...+ 97/3 + 98/2 +99/1
hãy tìm tỉ số T/M
Tính A = \(\frac{M}{N}\)biết
M =\(\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
N = \(N=\frac{92-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-...-\frac{90}{98}-\frac{91}{99}-\frac{92}{100}}{\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{495}+\frac{1}{500}}\)
2^100-2^99+2^98-2^97+...+2^2-2
3^100-3^99+3^98-3^97+...+3^2-3+1
Giúp với các bạn ơi!!!
1/2 + 2/3 + 3/4 + 4/5 + 5/6 + 6/7 + 7/8 + 8/9 + ........+ 95/96 + 96/97 + 97/98 + 98/99 + 99/100 = ?
