\(Cho\)\(P\)\(v\text{à}\)\(P+14\)\(l\text{à}\)\(hai\)\(s\text{ố}\)\(nguy\text{ê}n\)\(t\text{ố}\)
\(CMR:\)\(P+7\)\(l\text{à}\)\(h\text{ợp}\)\(s\text{ố}\)
\(Cho\)\(c\text{ác}\)\(s\text{ố}\)\(a,b,c,d,p\)\(l\text{à}\)\(c\text{ác}\)\(s\text{ố}\)\(nguy\text{ê}n\)\(t\text{ố}\)\(th\text{ỏa}\)\(m\text{ãn:}\)\(p=a+b=c-d.\)\(T\text{ìm}\)\(c\text{ác}\)\(s\text{ố}\)\(a,b,c,d\)\(v\text{à}\)\(p\)
\(Cho\)\(P=5+5^2+5^3+5^4+...+5^{102}\)
\(Ch\text{ứng}\)\(minh\)\(r\text{ằng:}\)\(P\)\(l\text{à}\)\(b\text{ội}\)\(c\text{ủa}\)\(6\)\(v\text{à}\)\(31\)
So sánh với n thuộc N*
\(\frac{n+1}{n+2}v\text{à}\text{ }\frac{n}{n-3}\)
So sánh :
\(10^{30}v\text{à}2^{100}\)
\(5^{300}v\text{à}3^{453}\)
\(29^{12}v\text{à}18^{17}\)
So sánh:
a)\(3^{200}v\text{à}2^{300}\)
b) \(71^{50}v\text{à}37^{75}\)
c) \(\frac{2016014}{2017015}v\text{à}\frac{2016016014}{2017017015}\)
\(\text{S=}\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{3}{27}+...+\dfrac{2019}{3^{2019}}ChứngminhS< \dfrac{3}{4}\)
\(A=\frac{20^{10}+1}{20^{10}-1}v\text{à}B=\frac{20^{10}-1}{20^{10}-3}Sos\text{á}nhAv\text{à}B\)
so sánh
\(10^{30}v\text{à}2^{106}\)
\(333^{444}v\text{à}444^{333}\)