\(A=3^{100}-3^{99}+3^{98}-...+3^2-3+1\)
\(3A=3\left(3^{100}-3^{99}+3^{98}-...+3^2-3+1\right)\)
\(3A=3^{101}-3^{100}+3^{99}-...+3^3-3^2+3\)
\(3A+A=\left(3^{101}-3^{100}+3^{99}-...+3^3-3^2+3\right)+\left(3^{100}-3^{99}+3^{98}-...+3^2-3+1\right)\)
\(4A=3^{101}+1\)
\(A=\dfrac{3^{101}+1}{4}\)
Thu gọn tổng sau :
a) \(A=1+3+3^2+3^3+...+3^{100}\)
b) \(B=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
c) \(C=3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\)
bn nào bt lm lm giúp mk vs
Thu gọn tổng sau :
a) \(A=1+3+3^2+3^3+...+3^{100}\)
b) \(B=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
c) \(C=3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\)
bn nào bt lm lm giúp mk vs
1.Tìm x y
3 mũ (x -1) + 5 x 3 mũ (x - 1) = 162
2.Rút gọn B = 3 mũ 100 - 3 mũ 99 + 3 mũ 98 - 3 mũ 97 + .... + 3 mũ 2 - 3 + 1
Tính:
a) S=1.2+2.3+3.4+...+99.100
b) B=\(\dfrac{49^{24}.125^{17}.2^8-5^{30}.7^{49}.4^5}{5^{29}.16^2.7^{48}}\)
c) C=\(\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}\right).3^5+\left(\dfrac{1}{3^5}+\dfrac{1}{3^6}+\dfrac{1}{3^7}+\dfrac{1}{3^8}\right).3^9+...+\left(\dfrac{1}{3^{97}}+\dfrac{1}{3^{98}}+\dfrac{1}{3^{99}}+\dfrac{1}{3^{100}}\right).3^{101}\)
d) D= \(3-3^2+3^3-3^4+...+3^{2017}-3^{2018}\)
Tính nhanh :
1)A=\(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)
2)B=\(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+...+\frac{1}{2^{99}}\)
3)C=\(\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+...-\frac{1}{2^{58}}\)
Tính giá trị của :
a) M = \(100^2-99^2+98^2-97^2+...+2^2-1^2\)
b) N = \(\left(20^2+18^2+16^2+...+4^2+2^2\right)-\left(19^2+17^2+15^2+...+3^2+1^2\right)\)
c) P = \(\left(-1\right)^n.\left(-1\right)^{2n+1}.\left(-1\right)^{n+1}\)
Bài 3: Tính giá trị của:
a) M = 1002 - 992 + 982 - 972 + ... + 22 - 12;
b) N = (202 + 182 + 162 + ... + 42 + 22) - (192 + 172 + 152 + ... + 32 + 12);
c) P = (-1)n.(-1)2n+1.(-1)n+1.
Bài 13: Tìm x biết:
a) (x - 1)3 = 27; e) 5x + 2 =625;
b) x2 + x = 0; f) (x - 1)x + 2 = (x - 1)x + 4;
c) (2x + 1)2 = 25; g) (2x - 1)3 = -8;
d) (2x - 3)2 = 36; h) 1/4 . 2/6 . 3/8 . 4/10 . 5/12 ... 30/62 . 31/64 = 2x.
Giúp mình với, đang cần gấp >_<
thục hiện phép tính
A = \(\dfrac{3}{1\times5}+\dfrac{3}{5\times10}+....+\dfrac{3}{100\times105}\)
B=\(\dfrac{5}{1\times3\times5}+\dfrac{5}{3\times5\times7}+...+\dfrac{5}{99\times101\times103}\)
Chứng tỏ
\(\dfrac{1}{3} + \dfrac{1}{3^2} +...+ \dfrac{1}{3^{99}}<1\)