A=1/2^2 +1/2^4 +1/2^6 +1/2^8 +⋯+1/2^100 CM: A<1/3
H24
Những câu hỏi liên quan
CM 1/4^2 + 1/ 6^2 + 1/8^2 +..... + 1/100^2 < 1/4
CM 1/4^2 + 1/ 6^2 + 1/8^2 +..... + 1/100^2 < 1/4
A=1/2^2 +1/3^2+1/4^2+...+1/100^2 và B=1/4^2+1/6^2+1/8^2+...+1/200^2. Tính A/B
A=1/2^2 +1/3^2+1/4^2+...+1/100^2 và B=1/4^2+1/6^2+1/8^2+...+1/200^2. Tính A/B
Cho A = 1/ 2^2 + 1/3^2 + 1/4^2 + .......+ 1/100^2 và B = 1/4^2 + 1/6^2 + 1/8^2 +........+ 1/200^2 . tính A/B = ........
\(B=\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+....+\frac{1}{200^2}=\frac{1}{\left(2.2\right)^2}+\frac{1}{\left(2.3\right)^2}+\frac{1}{\left(2.4\right)^2}+...+\frac{1}{\left(2.100\right)^2}\)
\(B=\frac{1}{2^2.2^2}+\frac{1}{2^2.3^2}+\frac{1}{2^2.4^2}+...+\frac{1}{2^2.100^2}=\frac{1}{2^2}.\frac{1}{2^2}+\frac{1}{2^2}.\frac{1}{3^2}+\frac{1}{2^2}.\frac{1}{4^2}+...+\frac{1}{2^2}.\frac{1}{100^2}\)
\(B=\frac{1}{2^2}.\left(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{100^2}\right)=\frac{1}{4}.A\)
\(\Rightarrow\frac{A}{B}=\frac{A}{\frac{1}{4}A}=\frac{A}{\frac{A}{4}}=A.\frac{4}{A}=4\)
Đúng 0
Bình luận (0)
A = 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2 và B = 1/4^2 + 1/6^2 + 1/8^2 + ...1/200^2. Khi đó A/B = ...
Cho A=1/2^2+1/2^4+1/2^6+1/2^8+...+1/2^100. Chứng minh A<1/3
\(A=\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+\frac{1}{2^8}+...+\frac{1}{2^{100}}\)
\(4A=1+\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{98}}\)
\(3A=4A-A=1-\frac{1}{2^{100}}<1\)
\(A<\frac{1}{3}\)
Đúng 0
Bình luận (0)
Cho A= 1/2^2+ 1/2^4+ 1/2^6+ 1/2^8+...1/2^100. Chứng minh A< 1/3
Thu Thảo Vũ tick đúng cho mình nhé Thu Thảo Vũ
Đúng 0
Bình luận (0)
Cho A=1/1*2+1/3*4+1/5*6+...+1/99*100 CM 7/2<A<5/6