Mình giải thử xem đúng ko nha:

M=1/2²+1/3²+1/4²+....+1/20²

=1/2.2+1/3.3+1/4.4+.....+1/20.20

mà M<1/1.2+1/2.3+1/3.4+....+1/19.20

M<1/1-1/2+1/2-1/3+...+1/19-1/20

M<1-1/20

M<19/20<1

=>  M<1

rb29 657 

B1: để x là số nguyên thì: 5 chia hết cho 2x+1

=> \(2x+1\in U\left(5\right)\)

+> \(2x+1\in\left\{1;-1;5;-5\right\}\)

=> \(x\in\left\{0;-1;2;-3\right\}\)

xc{0;-1;2;-3}

HT

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a, (sửa đề )

\(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{x.\left(x+1\right)}=\frac{1999}{2000}\)

=\(1+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{x.\left(x+1\right)}\right)=\frac{1999}{2000}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{x+\left(x+1\right)}=1-\frac{1999}{2000}=\frac{1}{2000}\)

=\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{2000}\)

=\(\frac{1}{1}-\frac{1}{x+1}=\frac{1}{2000}\)

=\(\frac{1}{x+1}=\frac{1}{1}-\frac{1}{2000}=\frac{1999}{2000}\)

=> \(x+1=1:\frac{1999}{2000}=\frac{2000}{1999}\)

=>\(x=\frac{2000}{1999}-1=\frac{1}{1999}\)

Vậy x ∈{ \(\frac{1}{1999}\)}

b, \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+.....+\frac{2}{x+\left(x+1\right)}=\frac{2}{9}\)

=> \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+.....+\frac{2}{x+\left(x+1\right)}=\frac{2}{9}\)

=>\(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+.....+\frac{2}{x+\left(x+1\right)}=\frac{2}{9}\)

=>2.(\(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+....+\frac{1}{x.\left(x+1\right)}\))=\(\frac{2}{9}\)

=>\(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+....+\frac{1}{x+\left(x+1\right)}=\frac{2}{9}:2=\frac{1}{9}\)

=>\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+....+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)

=>\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

=>\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\)

=>\(x+1=18\)

=>\(x=18-1=17\)

=>x∈{17}

1999 phần bao nhiêu vậy bạn ?

xin lỗi mik ghi thiếu
là 1999/2000

m= 2

n=7

1, x - [42 + (-28)] = -8

=> x - 14 = -8

=> x = -8 + 14

=> x = 6

Vậy x = 6

3, 4^x = 64

=> 4^x = 4³

=> x = 3 (vì cùng cơ số 4 > 1)

Vậy x = 3

4, 9^{x - 1} = 9

=> 9^{x - 1} = 9¹

=> x - 1 = 1 (vì cùng cơ sộ̣́ 9 > 1)

=> x = 1 + 1

=> x = 2

Vậy x = 2