Ta có:
\(P=\frac{2!}{3!}+\frac{2!}{4!}+\frac{2!}{5!}+...+\frac{2!}{n!}\)
\(=2!.\left(\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}+...+\frac{1}{n!}\right)\)
Ta thấy:
\(\frac{1}{3!}
Thùy dung ơi
\(\frac{1}{3!}=\frac{1}{2.3}\)nha.
3!=1.2.3=6
2.3=6
Chứng minh rằng:
a)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2010^2}\)<1
b)\(\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+\frac{4}{2^4}+...+\frac{100}{2^{100}}\)<2
c)\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\)<\(\frac{3}{4}\)
d)\(\frac{1}{3^3}+\frac{1}{4^3}+\frac{1}{5^3}+...+\frac{1}{n^3}\)<\(\frac{1}{12}\)\(\left(n\in N;n\ge3\right)\)
e)\(\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+...+\frac{2n+1}{n^2\left(n+1\right)^2}\)<1 (n nguyên dương)
g)\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{2048}\)>3
h)\(\left(\frac{2}{1}\right)\left(\frac{4}{3}\right)\left(\frac{6}{5}\right)...\left(\frac{200}{199}\right)\)
a) Chứng minh rằng: \(\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+...+\frac{1}{\left(2n+1\right)^2}< \frac{1}{4}\) với \(n\in N\) và \(n\ge1\)
Chứng minh rằng :
B=\(\frac{36}{1.3.5}+\frac{36}{3.5.7}+...+\frac{36}{25.27.29}<3\)
C= \(\frac{1}{4^2}+\frac{1}{6^2}+....+\frac{1}{\left(2n\right)^2}<\frac{1}{4}\left(n\in N;n\ge2\right)\)
Giúp mik nhé
Chứng minh rằng
\(G=\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+....+\frac{2n+1}{n^2.\left(n+1\right)^2}
Chứng minh rằng:\(\frac{1}{4^2}+\frac{1}{6^2}+\frac{1}{8^2}+...+\frac{1}{\left(2n^2\right)}< \frac{1}{4}\)( N \(\in\)N; n\(\ge\)2 )
Chứng minh rằng:
a)\(\frac{1.3.5...39}{21.22.23...40}=\frac{1}{2^{20}}\)
b)\(\frac{1.3.5...\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right)...2n}=\frac{1}{2^n}\)với n thuộc N*
Chứng minh rằng:
\(\frac{1.3.5.7.9.....\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\left(n+3\right).....2n}=\frac{1}{2^n}\)
Cho \(Q=\frac{5}{7}.\frac{13}{7^2}.\frac{97}{7^4}.....\frac{3^{2^{99}}+2^{2^{99}}}{7^{2^{99}}}\)
Chứng minh rằng: \(Q.\left(7^{2^{100}-1}\right)\in N\).
