Ta có :
1/2! + 2/3! + 3/4! + ... + 99/100!
\(=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{4!}+...+\frac{100-1}{100!}\)
\(=\frac{1}{1!}-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}-\frac{1}{4!}+...+\frac{1}{99!}-\frac{1}{100!}\)
\(=1-\frac{1}{100!}< 1\)( đpcm )
CMR 1/2!+2/3!+3/4!+...+99/100!<1
cmr:1/2!+2/3!+3/4!+...+99/100!<1
Cho biểu thức : \(C=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}+\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\) CMR: \(C< \dfrac{3}{16}\)
CMR:1/2!+2/3!+3/4!+............+99/100!<1
CMR: \(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}< \dfrac{3}{16}\)
CMR: 100-(\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\))=\(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{99}{100}\)
CMR:
a,\(100\left(1+\frac{1}{2}+\frac{1}{3}+..........+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+........+\frac{99}{100}\)
CMR
1/2! + 2/3! + 3/4! +...+ 99/100! <1
Mn giúp m vs
CMR: 3^1 + 3^2 +3^3 ...+ 3^99 + 3^100 chia hết cho 4
