\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\\ 2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\\ 2A+A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\\ 3A=2^{101}-2\)
Vậy \(A=\dfrac{2^{101}-2}{3}\)
Rút gọn : a) M = \(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
b) N = \(3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\)
Rút gọn a) M= 2100 - 299 + 298 - 297 +.....+ 22 - 2
b) N= 3100 - 399 + 398 - 397 +.....+ 32 - 3 + 1
\(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-1\)
(100^2 + 98^2 + 96^2 + ... +4^2 + 2^2 ) - (99^2 + 97^2 + 95^2 + ... + 3^2 + 1^2 )
Rút gọn: M=\(2^{100}-2^{99}+2^{98}-2^{97}+....+2^2-2\)
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
1002 - 992 + 982 - 972 + .... + 22 - 12
\(\frac{\frac{2000}{11}+\frac{2000}{12}+...+\frac{2000}{100}}{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{98}{2}+\frac{99}{1}}\)
Hãy rút gọn
bài 1: Cho A ( x ) = x99 - 100x98 + 100x97 - 100x96 +...+ 100x-1 . Tính A ( 99 )
bài 2: Cho P(x) = 100x100 + 99x99 +...+ 2x2 + x . TÍnh P(1)
