c;=(50-49)(50+49)+(48-47)(48+47)+.............+(2+1)(2-1)

=50+49+48+............+1

=(50+1)50=2550:2=1275

d;=(2^4-1)(2^4+1)(2^8+1)(2^16+1)

=(2^8-1)(2^8+1)(2^16+1)

=(2^16-1)(2^16+1)

=2^32-1

e;=(3-1)(3+1)(3^2+1)...........(3^16+1)

=(3^2-1)(3^2+1)..............(3^16+1)

=(3^16-1)(3^16+1)=3^32-1

tu tinh ket qua luy thua tao khong thua hoi dau

a) \(A=5^4.3^4-\left(15^2-1\right)\left(15^2+1\right)=\left(5.3\right)^4-\left(\left(15^2\right)^2-1^2\right)\)

\(=15^4-\left(15^4-1\right)=15^4-15^4+1=1\)

b) \(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)

\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+...+\left(2^2-1^2\right)\)

\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48+47\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=1.99+1.95+...+1.3=99+95+...+3\)

\(=\left(99+3\right)+\left(95+7\right)+...+\left(55+47\right)+51\)

\(=102+102+...+102+51\)

số lượng con số \(102\) là \(\dfrac{25-1}{2}=12\)

\(\Rightarrow C=102.12+51=1224+51=1275\)

\(B=\dfrac{1}{49}+\dfrac{2}{48}+\dfrac{3}{47}+...+\dfrac{48}{2}+\dfrac{49}{1}\)

\(B=\left(\dfrac{1}{49}+1\right)+\left(\dfrac{2}{48}+1\right)+\left(\dfrac{3}{47}+1\right)+...+\left(\dfrac{48}{2}+1\right)+\dfrac{49}{1}\)

\(B=\left(\dfrac{50}{49}+\dfrac{50}{49}+\dfrac{50}{48}+\dfrac{50}{47}+...+\dfrac{50}{2}\right)+1\)

\(B=\dfrac{50}{50}+\dfrac{50}{49}+\dfrac{50}{49}+\dfrac{50}{48}+\dfrac{50}{47}+...+\dfrac{50}{2}\)

\(B=50\left(\dfrac{1}{50}+\dfrac{1}{49}+\dfrac{1}{48}+...+\dfrac{1}{2}\right)\)

\(\Rightarrow\dfrac{A}{B}=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}}{50\left(\dfrac{1}{50}+\dfrac{1}{49}+\dfrac{1}{48}+...+\dfrac{1}{2}\right)}=\dfrac{1}{50}\)

1 ) a ) \(A=53^2+106.47+47^2=53^2+2.53.47+47^2=\left(53+47\right)^2=100^2=10000\)

b ) Sai đề

c ) \(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)

\(=\left(50-49\right)\left(50+49\right)+\left(49-48\right)\left(49+48\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=50+49+48+47+...+2+1\)

\(=\dfrac{50.51}{2}\)

\(=1275\)

2 ) a ) \(\left(x+3y\right)\left(x^2-3xy+y^2\right)=x^3+27y^3\)

b ) \(\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)=8x^3-27y^3\)

a) 53² - 106.47+ 47² hả cậu

Nếu thế thì : A = 53² + 2.53.47 + 47²

A = ( 53+47 ) ² = 100² =10000

Điền kí hiệu toán học vào tất cả chỗ trong 3 số tự nhiên này : 10 10 10=6

còn cần k

C=50² - 49² +48² -47² +...+2² -1²

=(50² - 49²)+(48² -47² )+.....+(2²-1)(

= (50 - 49)(50 + 49) + (48 – 47)(48 + 47) + ... +

(2 + 1)(2 – 1)

=(50+49).1+(48+47).1+.....+(2+1).1

= 50 + 49 + 48 + 47 + ... + 2 + 1

= (50 + 1) + (49 + 2) + ... + (25 +26)

= 51 . 25 = 1275