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
Những câu hỏi liên quan
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 1/4<M<4/9
Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang 1/4<M<4/9
Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang 1/4<M<4/9
cho a=1=1\2+1\3-1\4+1\5...+1\49-1\50.Chung to rang 7\12<4<5\6
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
Cho A = 1/32+1/42+1/52+.....+1/502 . Chứng minh rằng :
a) A > 1/4
b) A < 4/9
Phần a, A> 1/3.4+1/4.5+1/5.6+...+ 1/50.51 = 1/3-1/4+1/4-1/5+1/5-1/6+...+ 1/50-1/51 = 1/3-1/51 = 48/153 > 48/192 =1/4. ĐPCM
Phần b, A< 1/3^2+1/3.4+1/4.5+...+1/49.50 = 1/9+1/3-1/4+1/4-1/5+...+ 1/49-1/50 = 1/9+1/3-1/50 = 1/9+47/150 < 1/9+50/150 = 1/9+1/3 = 4/9. ĐPCM
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CHo A=1/3^2+1/4^2+1/5^2+...+1/50^2. Chứng tỏ rằng 1/4<A<4/9
Cho A = 1/32+1/42+1/52+.....+1/502 . Chứng minh rằng :
a) A > 1/4
b) A < 4/9
Ta có
\(A>\frac{1}{3^2}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{50.51}\)
\(\Rightarrow A>\frac{1}{9}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{50}-\frac{1}{51}\)
\(\Rightarrow A>\frac{1}{4}+\left(\frac{1}{9}-\frac{1}{51}\right)\)
\(\Rightarrow A>\frac{1}{4}+\frac{42}{9.51}>\frac{1}{4}\)
Vậy A>1/4
b)
Ta có
\(A< \frac{1}{3}^2+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{49.50}\)
\(\Rightarrow A< \frac{1}{9}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{59}-\frac{1}{50}\)
\(\Rightarrow A< \frac{4}{9}-\frac{1}{50}< \frac{4}{9}\)
Vậy A<4/9
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