a,A=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2.chung minh rang a<2
b;2^1+2^2+2^3+...+2^30.chung minh rang B chia het cho21
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cho A=\(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+.....+\frac{1}{50^2}\)
Chung minh rang A<2
mỗi p/số của A đều bé hơn 1/1.2+1/2.3+1/3.4+......+1/49.50
A<1-1/2+1/2-1/3+1/3-1/4+..........+1/49-1/50(tách ra thành hiệu)
A<1-1/50
mà 1/50>0=>1-1/50<1<2
A<1-1/50<1<2
A<2
chúc học tốt
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Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang a,A>1=4 b,A>4/9
Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang a,A>1=4 b,A>4/9
cho ak=1-4/(ak+1)2. Chung minh rang T=a1a2a3...a50>1/3
Cho A=1+1/2+1/3+...+1/2^100-1
chung minh rang:
a,A<100
b,A>50
CHO A=\(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{50^2}\)
CHUNG MINH RANG A<2
\(A<\frac{1}{1\cdot2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49\cdot50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}<1<2\)
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chung minh rang A = 1/2 + 1/3 + 1/4 +...+ 1/50 khong phai la so tu nhien
Cho A=1/2^2+1/3^2+1/4^2+.......+1/20^2 .Chung to rang A<1
Cho A=1/2^2+1/3^2+1/4^2+........+1/20^2 .Chung minh A<1
Chu thich / La phan so
^ la mu
\(Ta\)có :
\(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};...;\frac{1}{20^2}< \frac{1}{19.20}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{20^2}< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\)
\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}\)
\(\Rightarrow A< 1-\frac{1}{20}< 1\left(Đpcm\right)\)
Chúc bạn học tốt !!!
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Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang 1/4<M<4/9