bài 2:

\(A=9.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{98.99}+\dfrac{1}{99.100}\right)\)

\(A=9.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{98}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(A=9.\left(1-\dfrac{1}{100}\right)=9.\left(\dfrac{100}{100}-\dfrac{1}{100}\right)=\dfrac{891}{100}\)

bài 3:

\(=>\dfrac{x}{3}=\dfrac{5}{8}+\dfrac{1}{8}=\dfrac{8}{8}=1=\dfrac{3}{3}\)

\(=>x=3\)

Ta có A=1.2+2.3+3.4+...+98.99

B=1^2+2^2+3^2+...+98^2=1.1+2.2+3.3+...+98.98

=> A-B=(1.2+2.3+3.4+...98.99)-(1.1+2.2+3.3+...+98.98)

=(1.2-1.1)+(2.3-2.2)+(3.4-3.3)+...+(98.99-98.98)

=1.(2-1)+2.(3-2)+3.(4-3)+...+98.(99-98)

=1.1+2.1+3.1+...98.1

=1+2+3+...+98=[98.(98+1)]/2=98.99/2=4851

đúng nha

Ta có:a=1.2+2.3+3.4+...+98.99

a=1(1+1)+2(2+1)+3(3+1)+...+98(98+1)

a=1²+1+2²+2+3³+3+...+98²+98

a=b+(1+2+3+4+...+98)

a=b+(1+98).98:2

a=b+4851

Vậy a-b =4851

Ta có A =1.2 + 2.3 + 3.4 + ...+ 98.99 
B = 1^2 + 2^2 + 3^2 +...+98^2 = 1.1+2.2+3.3+...+98.98 
Suy ra: A-B= (1.2 + 2.3 + 3.4 + ...+ 98.99) - (1.1+2.2+3.3+...+98.98) 
= (1.2-1.1) + (2.3-2.2) + (3.4-3.3) +...+ (98.99-98.98) 
= 1(2-1) + 2(3-2) + 3(4-3) +...+ 98(99-98) 
= 1.1 + 2.1 + 3.1 +...+ 98.1 
= 1+ 2+ 3+...+ 98 = [98.(98+1)]/2= 98.99/2 = 4851

đúng nha

A = 1.2 + 2.3 + 3.4 + ... + 98.99

   = 1.(1 + 1) + 2.(2 + 1) + 3.(3 + 1) + ... + 98.(98 + 1)

   = 1² + 1 + 2² + 2 + 3² + 3 + ... + 98² +98

   = (1² + 2² + 3² + ... + 98²) + (1 + 2 + 3 + ... + 98)

   = B + (1 + 98).98 : 2

   = B + 4851

Do đó A = B + 4851 suy ra A - B = 4851

                     Kết luận : A - B = 4851 

A - B = 1+2+3+4+...+99

=99.(99+1)/2

=99.100/2

=99.50

=4950

\(\text{a=1.2+2.3+3.4+......+98.99}\)

\(=1\left(1\text{+}1\right)\text{+}2\left(2\text{+}1\right)\text{+}3\left(3\text{+}1\right)\text{+}.........\text{+}98\left(98\text{+}1\right)\)

\(=1^2\text{+}1\text{+}1^2\text{+}2\text{+}3^2\text{+}3\text{+}...\text{+}98^2\text{+}98\)

\(=b\text{+}\left(1\text{+}2\text{+}3\text{+}...\text{+}98\right)\)

\(=b\text{+}\left(98\text{+}1\right).98:2\)

\(=b\text{+}4851\)

\(\Rightarrow a-b=4851\)

dễ ợt

nhanh tích cho nhee

tui làm b nha do a không biết làm

A=5+3²+3³+...+3²⁰¹⁸

3A=15+3³+3⁴+...+3²⁰¹⁹

3A-A=(15+3³+3⁴+...+3²⁰¹⁹)-(5+3²+3³+...+3²⁰¹⁸)

2A=3²⁰¹⁹+15-(5+3²)

2A=3²⁰¹⁹+15-14

2A=3²⁰¹⁹+1

2A-1=3²⁰¹⁹+1-1

2A-1=3²⁰¹⁹

vậy n = 2019

cmon nhaa, mỗi câu b thoi cx đc :3