1/2! + 2/3! + 3/4! + ... + 99/100!
<1/1.2 + 1/2.3 + 1/3.4 + ... + 99/99.100 = 1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
= 1 - 1/100 <1
=> 1/2! + 2/3! + 3/4! + ... + 99/100! < 1
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,\(100\left(1+\frac{1}{2}+\frac{1}{3}+..........+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+........+\frac{99}{100}\)
cho bt: \(C=\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}.\)CMR: C<\(\frac{3}{16}\)
CMR:\(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)
CMR: \(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)
\(CMR:\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+.....+\frac{99}{100!}< 1\)
\(CMR:\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\frac{4}{5!}+................+\frac{99}{100!}<1\)
CMR
\(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{\text{4!}}+...+\frac{99}{100!}< 1\)
\(CMR:\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+............+\frac{99}{100!}<1\)
