Ta có:
S = 1/22 + 1/32 + 1/42 + ... + 1/20162
= 1/2.2 + 1/3.3 + 1/4.4 + ... + 1/2016.2016
S < 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/2015.2016
S < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2015 - 1/2016
S < 1 - 1/2016
Mà 1 - 1/2016 < 1
=> S < 1
Vậy S < 1
Ủng hộ nha
\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2017}}\)
chứng tỏ A<1
2,
\(S=2+2^2+2^3+...+2^{99}\)
C/t: S chia hết cho 7, 31
3,
\(A=1+5+5^2+5^3+5^4+5^5+...+5^{99}+5^{100}\)
Tính A
4,
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)<1
5,
CHỨNG tỏ rằng các p/s tối giản vs mọi số tự nhiên n
a,\(\frac{n+1}{2n+3}\)b,\(\frac{2n+3}{4n+8}\)
6,
a,TÍnh A và B
A=\(\frac{2016^{2016}+2}{2016^{1016}-1}\)B=\(\frac{2016^{2016}}{2016^{2016}-3}\)
b, tính
C=\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)
LÀm NHANH Hộ MK ,MAi mk Phải Nộp.
Cho S=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{30}}\)
Chứng tỏ: S<1
Cho S = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2012}}+\frac{1}{2^{2013}}\) Chứng tỏ S < 1
Cho \(S=\frac{1}{4}+\frac{2}{4^2}+\frac{3}{4^3}+...+\frac{2016}{4^{2016}}\)
Chứng minh rằng : \(S<\frac{1}{2}\)
Cho S = \(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}\). Chứng tỏ rằng 1/6 < S < 1/4
Cho S = \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2018}}\)
Chứng tỏ rằng S < 1
chứng tỏ \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2016}}+\frac{1}{2^{2017}}< 1\)
Chứng tỏ rằng: \(\frac{49}{100}< S=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{99^2}\)<1
chứng minh S = \(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\)
