\(A=1+5+5^2+5^3+...+5^{49}+5^{50}\)
=> \(5\text{A}=5+5^2+5^3+5^4...+5^{49}+5^{50}+5^{51}\)
=> \(5\text{A-A}=5+5^2+5^3+5^4...+5^{49}+5^{50}+5^{51}\) - (\(1+5+5^2+5^3+...+5^{49}+5^{50}\) )
=> \(5\text{A-A}=5+5^2+5^3+5^4...+5^{49}+5^{50}+5^{51}\) - \(1-5-5^2-5^3-...-5^{49}-5^{50}\)
=> \(4\text{A}=5^{51}-1\)
=> \(A=\dfrac{5^{51}-1}{4}\)
Tính:
A = \(1+5+5^2+5^3+...+5^{49}+5^{50}\)
Rút gọn : B = \(( -5 ) ^0 + ( -5 ) ^ 1 + (-5)^2+(-5)^3+....+(-5)^{49}+(-5)^{50}\)
x : [8/5.2/3^2 - 2/5]=15/7+6/5[(15/7)^2-50/49]
bài 1: tính A:=\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}+\frac{5}{6}-\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{2}{3}-\frac{1}{2}\)
Bài 2: Cho B=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{49}-\frac{1}{50}\)
Chứng minh rằng: \(\frac{7}{12}< A< \frac{5}{6}\)
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!!
2 TÌM X BIẾT
a, (5x+1)^2 = 36/49
b, (12/25)^x =(5/3)^2 -(-3/5)^4
c, (-3/4)^ 3x-1 = 256/81
d, 172 .x ^2 -7^9 :98^3 =2^3
e,5^x .(5^3)^2 =625
f, (x-2/9)^3 =(2/3)^6
Thực hiện phép tính:
\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(B=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\dfrac{2^2}{7^2}-\dfrac{4}{343}}\)
Thực hiện phép tính
a, A = \(\left(\dfrac{1}{4\times9}+\dfrac{1}{9\times14}+\dfrac{1}{14\times19}+....+\dfrac{1}{44\times49}\right)\times\dfrac{1-3-5-7-....-49}{89}\)
b, B = \(\dfrac{2^{12}\times3^5-4^6\times9^2}{\left(2^2\times3\right)^6+8^4\times3^5}-\dfrac{5^{10}\times7^3-25^5\times49^2}{\left(125\times7\right)^3-5^9\times14^3}\)
tìm x,y, z
a,1/2x =3/4z= 2/3y và x-y =15
b, x-1/2 =y-2/3=z-3/4 và 2x+3y -z= 50
c, 2x/3 =3y/4=4z/5 và x+y+z=49