\(\left(50^2-49^2\right)+\left(48^2-47^2\right)+\left(46^2-45^2\right)+...+\left(2^2-1^2\right)\)

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

\(+\left(4-3\right)\left(4+3\right)+\left(2-1\right)\left(2+1\right)\)

(ta thấy trong mỗi tích đều có 1 thừa số bằng 1, VD: 50-49=1)

\(A=99+95+91+...+7+3\) số hạng cách nhau 4 đơn vị

Số số hạng của A là \(\left(99-3\right):4+1=25\)

=> \(A=\left(99+3\right).25:2=1275\)

Theo bài ra ta có:

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

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

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

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

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

\(=\left(50+49\right)\times50\div2=2475\)

Vậy giá trị biểu thức = 2475

C = 50 - 49 + 48 - 47 + ... + 2 - 1 ( có 50 số hạng )

=> C = ( 50 - 49 ) + ( 48 - 47 ) + ... + ( 2 - 1 ) ( có đủ 25 nhóm )

=> C = 1 + 1 + ... + 1 ( 25 số hạng 1 )

=> C  = 1 . 25 = 25

(50-1):1+1=50 số

=(50-49)+(48-47)+...+(4-3)+(2-1). Ta có 25 cặp số

=1+1+1+....+1

=1.25

=25

vậy còn phần B bạn ơi giải lun cho mk đi 

A= 50-49+49-48+48-47+......+3-2+2-1

A=50-1

A=49

B=50-49+48-47+46-45+.....+4-3+2-1

B=(50-49)+(48-47)+(46-45)+.....+(4-3)+(2-1)

B= 1+1+1+.....+1+1

B=1x25

B=25

Mình không chắc chắn lắm đâu nhé!

a,87^2 + 26.87 +13^2

=87.(87+26) + 13^2

=87.113 + 169

=10000

a) \(87^2+26\cdot87+13^2=87^2+2\cdot87\cdot13+13^2=\left(87+13\right)^2=100^2=10000\)

Sủa đề : tính \(D=\left(50^2+48^2+46^2+....+2^2\right)-\left(49^2+47^2+45^2+...+1^2\right)\)

\(=\left(50^2-49^2\right)+\left(48^2-47^2\right)+\left(46^2-45^2\right)+.....+\left(2^2-1^2\right)\)

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

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

\(=\frac{50\left(50+1\right)}{2}=1275\)

D=(50²-49²)+(48²-47²)+...+(2²-1²)

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

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

=\(\frac{\left(50+1\right).50}{2}\)

=1275

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

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

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

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

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

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