\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right)...............\left(1+\frac{1}{100}\right)\)
\(=\frac{3}{2}.\frac{4}{3}...............\frac{101}{100}\)
\(=\frac{3.4..................101}{2.3..................100}\)
\(=\frac{101}{2}=50,5\)
1. (1+1/2).(1+1/2^2).(1+1/2^3)....(1+1/2^100) < 3
2. 1/(5+1)+2/(5^2+1)+4/(5^4+1)+...+ 1024/(5^1024+1) <1/4
3. 3/(1!+2!+3!)+4/(2!+3!+4!)+...+100/(98!+99!+100!) <1/2
CMR:
a)1/10^2 +1/11^2+1/12^2+...+1/100^2 >3/4
b)1/2^2+1/3^2+1/4^2+...+1/100^2<99/100
c)1/2^2+1/3^2+1/4^2+...+1/100^2<3/4
Tính tổng 100-(1+1/2+1/3+1/4+...+1/100)/1/2+2/3+3/4+....+99/100
1/1*2-1/1*2*3+1/2*3-1/2*3*4+1/3*4-1/3*4*5+...+1/99*100-1/99*100*101
chứng minh : 100- (1+1/2+1/3+1/4+...+1/100)=1/2+2/3+3/4+...+99/100
100-(1+1/2+1/3+1/4+...+1/100)
1/2+2/3+3/4+...+99/100
Tính:
A=(1-1/1+2).(1-1/1+2+3).(1-1/1+2+3+4)...(1-1/1+2+3+4+...+2022)
B=1+1/2(1+2)+1/3(1+2+3)+1/100(1+2+3+...+100)
chứng minh 100-(1+1/2+1/3+1/4+...+1/100)=1/2+1/3+1/4+...+99/100
M=1 + 1/2 (1+2) + 1/3 (1+2+3) +1/4 (1+2+3+4) +...+ 1/100. (1+2+3+...+100) = ?
CMR:(1+1/2+1/3+1/4+...+1/100)=1/2=2/3+3/4+...+99/100
