Chung minh 1/2^2+1/3^2+...+1/50^2<1?
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
A=1/2^2+1/3^2+...+1/50^2 , chung minh A<1
Chung minh
A=1/2+1/2^2+15/2^3+....+1/2^50<1
ChoA=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2
Chung minh A <2
\(A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}< 1< 2\Rightarrow A< 2\Rightarrowđpcm\)
\(A=\frac{1}{1^2}+\frac{1}{2^2}+.....+\frac{1}{50^2}\)
\(< 1+\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{49.50}\)
\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{49}+\frac{1}{50}\)
\(=2-\frac{1}{50}< 2\)
Vậy A<2
Chung minh A < 2:
A=1/1^2+1/2^2+1/3^2+1/4^2+.....+1/50^2
Cho A = 1/3^2 + 1/4^2 + 1/5^2 +...+ 1/50^2
Chung minh 1/4 < A < 4/9
chung minh rang:1/(1*2)+1/(3*4)+1/(5*6)+.....+1/(49*50)=1/26+1/27+1/28+....+1/50
CHO A=\(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{50^2}\)
CHUNG MINH RANG A<2
\(A<\frac{1}{1\cdot2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49\cdot50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}<1<2\)
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