Violympic toán 8
Các câu hỏi tương tự
CMR: 1 - 1/2+ 1/3 -1/4+......+1/99-100 = 1/101 + 1/102+......+1/200
Tính :
a ) \(S=\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+.....+\dfrac{1}{\sqrt{100}+\sqrt{101}}\)
b ) \(S=\dfrac{1}{\sqrt{2}+\sqrt{4}}+\dfrac{1}{\sqrt{4}+\sqrt{6}}+...+\dfrac{1}{\sqrt{100}+\sqrt{102}}\)
Tính
A=1/2+1/2^2+1/2^3+...+1/2^100
Tính
B=1/2+1/2^2+1/2^3+1/2^4+...+1/2^99 - 1/2^100
Tính
C=1/2+1/2^3+1/2^5+...+1/2^99
Tính
D=2/3+8/9+26/27+...+3^n-1/3^n.Chứng minh A>n-1/2
Tính: E=4/3+10/9+28/27+...+3^39+1/3^92.Chứng minh B<100
Tính
F=5/4+5/4^2+5/4^3+...+5/4^99.Chứng minh C<5/3
Tính
G=3/1^2*2^2+5/2^2*3^2+7/3^2*4^2+...+19/9^2*10^2.Chứng Minh D<1
B=1/2+1/2^2+1/2^3+1/2^4+...+1/2^99 - 1/2^100
C/M 1+2+22+....+299+2100=2101-1
Tính:
A= -1^2+2^3-3^2+4^2....-99^2+100^2
B=(2+1).(2^4+1).(2^8+1).(2^16+1)
Tìm x:
\(\dfrac{x-5}{100}+\dfrac{x-4}{100}+\dfrac{x-3}{100}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)
\(\dfrac{29-x}{21}+\dfrac{27-x}{23}+\dfrac{25-x}{25}+\dfrac{23-x}{27}+\dfrac{21-x}{29}=-5\)
\(\dfrac{2-x}{2001}-1=\dfrac{1-x}{2002}-\dfrac{x}{2003}\)
Cho M= \(\dfrac{2^3-1}{2^3+1}\).\(\dfrac{3^3-1}{3^3+1}\).\(\dfrac{4^3-1}{4^3+1}\)......\(\dfrac{100^3-1}{100^3+1}\)
Cmr: M>\(\dfrac{2}{3}\)
Bài 2: Tính
a) 1002-992+982-972+....+22-1
b)(3+1)(32+1)(34+1)(38+1)(316+1)
c)3(22+1)(24+1).....(264+1)+1