nhanh ho mik mai cha bai roi
ai nhanh nhat mik k
nhung phai dung
Đúng 0
Bình luận (0)
Các câu hỏi tương tự
So sánh với n thuộc N*
\(\frac{n+1}{n+2}v\text{à}\text{ }\frac{n}{n-3}\)
so sánh a)\(\frac{10^{2014}-1}{10^{2015}-1}v\text{à}\frac{10^{2013}-1}{10^{2014}-1}\)
b) \(\frac{n+3}{n-2}v\text{à}\frac{n+5}{n-4}\)
\(sosanh\frac{n}{n+1}va\frac{3n+1}{6n+3}\)
Giải bằng phương pháp quy nạp
CMR với mọi n thuộc N* ta có:
\(a,1.2+2.3+...+n\left(n+1\right)=\frac{n\left(n+1\right)\left(n+2\right)}{3}\)
\(b,\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{2^n}=\frac{2^n-1}{2^n}\)
\(c,1^3+2^3+3^3+...+n^3=\frac{n^2.\left(n+1\right)^2}{4}\)
So sánh với n thuộc N*
\(\frac{2003\cdot2004-1}{2003\cdot2004}v\text{à}\frac{2004\cdot2005-1}{2004\cdot2005}\)
\(\frac{3535\cdot232323}{353535\cdot2323};\frac{3535}{3534}v\text{à}\frac{2323}{2322}\)
CMR \(\forall n\in\)N* ta có
\(\left(1-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+...+\left(\frac{1}{2n-1}-\frac{1}{2n}\right)=\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n}\)
\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)...\left(1+\frac{1}{n}\right)>\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n}\) không?
Chứng minh rằng:a)frac{1}{2^2}+frac{1}{3^2}+frac{1}{4^2}+...+frac{1}{2010^2}1b)frac{1}{2}+frac{2}{2^2}+frac{3}{2^3}+frac{4}{2^4}+...+frac{100}{2^{100}}2c)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(nin N;nge3right)e)frac{3}{4}+frac{5}{36}+frac{7}{144}+...+frac{2n+1}{n^2left(n+1right)^2}1 (n nguyên dương)g)frac{1}{31}+frac{1}{32}+frac{1}{33}+...+frac{1}{2048}3h)left(frac{2}{1}right)left(frac{4}{3}rig...
Đọc tiếp
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)\(\left(\frac{2}{1}\right)\left(\frac{4}{3}\right)\left(\frac{6}{5}\right)...\left(\frac{200}{199}\right)\)
So sánh:
a) \(A=\frac{n}{n+1};B=\frac{n+2}{n+3}\left(n\inℕ\right)\)
b) \(A=\frac{n}{n+3};B=\frac{n-1}{n+4}\left(n\inℕ^∗\right)\)
c) \(A=\frac{n}{2n+1};B=\frac{3n+1}{6n+3}\left(n\inℕ\right)\)
Giúp mình nhé gấp lắm ai trả lời đầu tiên mình sẽ tick