M = 1 + 2 + 3 + 4 + ... + (n - 3) + (n - 2) + (n - 1) + n
\(M=\frac{n\left(n+1\right)}{2}\)
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chứng minh rằng
1, 1/n(n+1)=1/n-1/n+1
2, 2/n(n+1)(n+2)=1/n(n+1)-1/(n+1)(n+2)
3, 3/n(n+1)(n+2)(n+3)=1/n(n+1)(n+2)-1/(n+1)(n+2)(n+3)
4, 4/(2n-1)(2n+1)(2n+3)=1/(2n+1)(2n-1)-1/(2n+1)(2n+3)
5, m/n(n+m)=1/n-1/n+m
6, 2m/n(n+m)(n+2n)=1/n(n+m)-1/(n+m)(n+2n)
chứng minh rằng
1, 1/n(n+1)=1/n-1/n+1
2, 2/n(n+1)(n+2)=1/n(n+1)-1/(n+1)(n+2)
3, 3/n(n+1)(n+2)(n+3)=1/n(n+1)(n+2)-1/(n+1)(n+2)(n+3)
4, 4/(2n-1)(2n+1)(2n+3)=1/(2n+1)(2n-1)-1/(2n+1)(2n+3)
5, m/n(n+m)=1/n-1/n+m
6, 2m/n(n+m)(n+2n)=1/n(n+m)-1/(n+m)(n+2n)
ai nhanh mình tick trước 9 giờ
a) F = 3/1.4 + 3/4.7 + 3/7.10 + ... + 3/n.(n+3) với n thuộc N*
b)M = 1/2 mũ 2 + 1/3 mũ 2 +1/4 mũ 2 +...+ 1/n mũ 2 < 1
c) N = 1/4 mũ 2 + 1/6 mũ 2 + 1/8 mũ 2+...+ 1/2n mũ 2 < 1/4 (với n thuộc N,n lớn hơn hoặc bằng 2)
d) P = 2!/3! + 2!/4! + 2!/5!+ ...+ 2!/n! <2 ( với n thuộc N,n lớn hơn hoặc bằng 2)
Cmr:
a)M=1/2^2+1/3^2+1/4^2+...+1/n^2<1 (neN;n>=2)
b)N=1/4^2+1/6^2+1/8^2+...+1/(2n)^2<1/4 (n€N,n>=2)
c)P=2!/3!+2!/4!+2!/5!+...+2!/n!<1 (n€N,n>=3)
Chứng minh rằng:a) A1/2^2+1/3^2+1/4^2+...+1/2010^21b) B1/2+2/2^2+3/2^3+...+100/2^1002c) C1/3+2/3^2+3/3^3+...+100/3^1003/4d) D1/2^3+1/3^3+1/4^3+...+1/n^31/4 (n€ N;n hoặc 3)e) E1/3^3+1/4^3+1/5^3+...+1/n^31/12 (n€N; n hoặc 3)f) F2/1*4/3*6/5*...*200/19920g) G3/4+5/36+7/144+...+2n+1/n^2*(n+1)^21 (n nguyên dương)h) H1/2*(1/6+1/24+1/60+...+1/9240)57/462i) I1/31+1/32+1/33+...+1/20483j) J(1-1/3)*(1-1/6)*(1-1/10)*...*(1-1/253)2/5k) K1/2!+2/3!+3/4!+...+n-1/n! (n€N;n hoặc 2)l) L1/2!+5/3!+11/4!+...+n^2+n-...
Đọc tiếp
Chứng minh rằng:
a) A=1/2^2+1/3^2+1/4^2+...+1/2010^2<1
b) B=1/2+2/2^2+3/2^3+...+100/2^100<2
c) C=1/3+2/3^2+3/3^3+...+100/3^100<3/4
d) D=1/2^3+1/3^3+1/4^3+...+1/n^3<1/4 (n€ N;n> hoặc = 3)
e) E=1/3^3+1/4^3+1/5^3+...+1/n^3<1/12 (n€N; n> hoặc = 3)
f) F=2/1*4/3*6/5*...*200/199<20
g) G=3/4+5/36+7/144+...+2n+1/n^2*(n+1)^2<1 (n nguyên dương)
h) H=1/2*(1/6+1/24+1/60+...+1/9240)>57/462
i) I=1/31+1/32+1/33+...+1/2048>3
j) J=(1-1/3)*(1-1/6)*(1-1/10)*...*(1-1/253)<2/5
k) K=1/2!+2/3!+3/4!+...+n-1/n! (n€N;n> hoặc = 2)
l) L=1/2!+5/3!+11/4!+...+n^2+n-1/(n+1)!<2
m) 1/6M=1/5^2+1/6^2+1/7^2+...+1/100^2<1/4
1. Chứng minh: \(\left(2^1+2^2+2^3+2^4+...+2^{59}+2^{60}\right):3\)
2. Chứng minh: \(M=3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}⋮6\)
1+ 2+ 3+ 4+ ......+( n - 3)+ (n - 2)+ (n - 1)+ n
MN GIÚP VS M ĐG CẦN GẤP
chứng tỏ rằng : M= 1/2^2 + 1/3^2 + 1/4^2 +...+1/n^2 <1 (với n>_ 2 n thuộc N )
Tìm m , n thỏa mãn
a,( m - 1) ( n - 2 ) = 4
b,(2m+1)(n-1)=5
c,(m-2)(n+3)=m+13
d,(m+3)(n+2)=2n+7