chung minh rang 1+1=3
a,A=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2.chung minh rang a<2
b;2^1+2^2+2^3+...+2^30.chung minh rang B chia het cho21
chung minh rang 1+1=3
chung minh rang (2n +1 ; 4n+3 ) =1
thiếu đè bài rồi
đề bài là chứng minh rằng ƯC [ 2n+1 ,4n+3] =1
hay chung minh rang A la so chinh phuong biet rang :A =1^3 + 2^3 + 3^3 + 4^3
\(A=1^3+2^3+3^3+4^3=1+8+27+64=100\)
Vì 100=102
=>A là số chính phương (đpcm)
A= \(1^3+2^3+3^3+4^3\)
A=1+8+27+54=90
VÌ 90=32
Vậy A là SCP (đpcm)
sai roi con bay dat tra loi 4^3 = 64 ma phai khong can tinh co neu tinh thi ai chang lam duoc
chung minh rang 11^n+2+12^2n+1 chia het cho 133
chung minh rang A=(17^n+1)(17^n+2)chia het cho 3 voi moi n thuoc N
cho (2a+7b) chia het cho 3 ( a b thuoc N). chung to (4a+2b) chia het cho 3
chung minh rang 1/2!+1/3!+1/4!+..................+1/100!<1
Đặt \(A=\dfrac{1}{2!}+\dfrac{1}{3!}+\dfrac{1}{4!}+...+\dfrac{1}{100!}\)
Ta thấy:
\(\dfrac{1}{2!}=\dfrac{1}{1.2};\dfrac{1}{3!}=\dfrac{1}{1.2.3}< \dfrac{1}{2.3};...;\dfrac{1}{100!}=\dfrac{1}{1.2...100}< \dfrac{1}{99.100}\)
Cộng vế với vế ta được:
\(A< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
\(\Rightarrow A< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(\Rightarrow A< 1-\dfrac{1}{100}< 1\)
Vậy \(\dfrac{1}{2!}+\dfrac{1}{3!}+\dfrac{1}{4!}+...+\dfrac{1}{100!}< 1\) (Đpcm)
\(\dfrac{1}{2!}+\dfrac{1}{3!}+\dfrac{1}{4!}+\dfrac{1}{100!}\)
\(=\left(\dfrac{1}{1!}-\dfrac{1}{2!}\right)+\left(\dfrac{1}{2!}-\dfrac{1}{3!}\right)+\left(\dfrac{1}{3!}-\dfrac{1}{4!}\right)+...+\left(\dfrac{1}{99!}-\dfrac{1}{100!}\right)\)
\(=1-\dfrac{1}{100!}< 1\)
cho C = 1 +3 + 32 + 33 + .... + 311 chung minh rang
a, chứng minh rằng C chia hết cho 13
b, chung minh rang C CHIA HET CHO 40
chung minh rang 1/2 +1/3 +1/4+....+1/63<5
chung minh rang 1/5^3+1/6^3+1/7^3+..........+1/2004^3<1/40