\(A=3^{100}-3^{99}+3^{98}-3^{97}+.........+3^2-3+1\)
\(\Leftrightarrow3A=3^{101}-3^{100}+3^{99}-3^{98}+......+3^3-3^2+3\)
\(\Leftrightarrow3A+A=\left(3^{101}-3^{100}+3^{99}-3^{98}+........+3^3-3^2+3\right)+\left(3^{100}-3^{99}+3^{98}-3^{97}+.......+3^2-3+1\right)\)
\(\Leftrightarrow4A=3^{101}+1\)
\(\Leftrightarrow A=\dfrac{3^{101}+1}{4}\)
Tính giá trị biểu thức A , biết rằng A = M : N
Mà M = \(\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+\dfrac{4}{96}+...+\dfrac{97}{3}+\dfrac{98}{2}+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
N = \(\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{90}{98}-\dfrac{91}{99}-\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+...+\dfrac{1}{495}+\dfrac{1}{500}}\)
B=3100-399+398-397+....+32-3+1
Tính: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-3\)
Tính tổng các dãy số sau
a.100-99+98-97+96-95+...+4-3+2-1
b.200-199+198-197+...+4-3+2-1
Rút gọn biểu thức:
\(N=3^{100}-3^{99}+3^{98}-...-3\)
a, Tính tổng A = 1 + 5 + 52 + 53 + ... + 52008 + 52009
b, B = 2100 \(-\) 299 + 298 \(-\) 297 + ... + 22
c, C = ( 1000 - 13 ) . ( 1000 - 23 ) . (1000 - 33 ) ... ( 1000 - 503)
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|
a,\(B=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+......+\dfrac{1}{3^{2004}}+\dfrac{1}{3^{2005}}\)
b,A=\(1+5+5^2+5^3+5^4+.....+5^{49}+5^{50}\)
c,A=\(\left(\dfrac{1}{2^2}-1\right).\left(\dfrac{1}{3^2}-1\right).\left(\dfrac{1}{4^2}-1\right).....\left(\dfrac{1}{100^2}-1\right)\)
d,A=\(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
Ai giúp mình thực hiện phép tính này với ạ?? Cảm ơn nhiều!!
Tính tổng
1,A=a1+a2+...+an với ai-ai-1=k
2,B=1/1*2*3+1/2*3*4+...+1/48*49*50
3,C=1+1/3+1/5+...+1/97+1/99
/
1/1*99+1/3*97+...+1/97*3+1/99*1
