Câu 1
a) x/5+y/3=13/15
Câu 2 tính
b) 1/1*2+1/2*3+1/3*4+...+1/n*n+1
c) 1/20+1/30+1/42+1/56+1/72+1/90+1/101
e) 1/2+1/2^2+1/2^3+1/2^4+...+1/2^9
g) 1/4+1/12+1/36+1/108+1/324+1/972
Câu 3 tìm các số nguyên dương x;y sao cho
a) x/10-1/y=3/10
b)1/x+y/2=5/8
câu 5 cho a=1/31+1/32+1/33+...+1/60
chứng minh A>7/12
câu 6 Cho A=1/3^2+1/4^2+1/5^2+1/6^2+...+1/50^2
chứng minh
a) A>1/4
b)A<4/9
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Câu 2:
b: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{n\left(n+1\right)}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n}-\dfrac{1}{n+1}\)
\(=1-\dfrac{1}{n+1}=\dfrac{n}{n+1}\)
c: \(\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{110}\)
\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-...+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=\dfrac{1}{4}-\dfrac{1}{11}=\dfrac{7}{44}\)