Ta có:
\(2^{150}=\left(2^3\right)^{50}=8^{50}\)
\(3^{100}=\left(3^2\right)^{50}=9^{50}\)
Vì \(8^{50}< 9^{50}\)
\(\Rightarrow\)\(2^{150}< 3^{100}\)
\(2^{150}\) và \(3^{100}.\)
Ta có:
\(2^{150}=\left(2^3\right)^{50}=8^{50}.\)
\(3^{100}=\left(3^2\right)^{50}=9^{50}.\)
Vì \(8< 9\) nên \(8^{50}< 9^{50}.\)
\(\Rightarrow2^{150}< 3^{100}.\)
Chúc bạn học tốt!
1+3/2^3+4/2^4+...+100/2^100
Cho \(A=1+\dfrac{3}{2^3}+\dfrac{4}{2^4}+\dfrac{5}{2^5}+...+\dfrac{100}{2^{100}}\). Chứng minh A < 2.
Chứng minh rằng : \(B=\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+\dfrac{4}{3^4}+...+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)
Tính a/2=b/3 và a.b=150
tính
A=1+\(\dfrac{3}{2^3}\)+\(\dfrac{4}{2^4}\)+\(\dfrac{5}{2^5}\)+.....+\(\dfrac{100}{2^{100}}\)
Cho \(A=1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2^{100}-1}\).
CMR: 50 <A < 100.
\(\dfrac{x^2}{9}=\dfrac{y^2}{16}và\)\(x^2+y^2=100\)
A=1+31+32+33+...+398+399+3100
(-1 1/2).(-1 1/3).(-1 1/4).....(-1 1/100)
