Lấy CUỐI CHỪ ĐẦU CHIA KHOANG CÁCH 

\(1+2-3-4+...+97+98-99-100\)

\(=\left(1+2-3-4\right)+...+\left(97+98-99-100\right)\)

\(=\left(-4\right)+...+\left(-4\right)\)            Vì dãy số trên có 100 số hạng => Dãy số trên có 25 cặp -4.

\(=\left(-4\right).25\)

\(=-100\)

Tk mk nhé!Thank you!

Có: 1+2-3-4+......+97+98-99-100

= 1+(2-3-4+5)+......+(94-95-96+97)+98-99-100

=1+98-99-100

=99-99-100

= -100

\(C=\frac{1}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\)

\(C=\frac{1}{100}-\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{99-98}{98.99}+\frac{100-99}{99.100}\right)\)

\(C=\frac{1}{100}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)

\(C=\frac{1}{100}-\left(1-\frac{1}{100}\right)=\frac{2}{100}-1=-\frac{49}{50}\)

bạn k trước mk mới kb

=1/125

A=1-2-3+4+5-6-7+8+...+97-98-99+100

=>A=(1-2-3+4)+(5-6-7+8)+...+(97-98-99+100)

=>A=0+0+....+0=0

vậy A=0

B=1-2+2^2-2^3+...+2^100

=>2B=2-2^2+2^3-2^4+....+2^101

=>2B+B=1-2^101=3B

=>B=1-2^101/3

C= 2^100-2^99-2^98-...-2^2-2-1

=>C=2^100-(2^99+2^98+.....+2^2+2+1)

Đặt D=2^99+2^98+.....+2^2+2+1

=>2D=2^100+2^99+.....+2^3+2^2+2

=>2D-D=2^100-1=D

=>C=2^100-(2^100-1)=1

tick nha

hic!ngày kia phải nộp rồi ! mọi người giúp mình nhanh nha!

1+2-3-4+.....+97+98-99-100 nhanh len 

18576: {\(105^0\)+[2.(102+101−100−99+98+97−96−95+.........+6+5−4−3+2+1)−201]}^3

Đặt A=102+101−100−99+98+97−96−95+...............+6+5−4−3+2+1

A=(102+101−100−99)+(98+97−96−95)+........+(6+5−4−3)+2+1

A=4+4+...........+4+3

A=4.25+3

A=103

⇒18576:{1050+[2.(102+101−100−99+98+97−96−95+.........+6+5−4−3+2+1)−201]}^3

=18576:[1+(2.103)−201]^3

=18576:63

=18576:216

=86

bằng 86 bn nhé

=86 nhé 

Đặt S = 2.4 + 4.6 + 6.8 + .... + 98.100 + 100.102

<=> S = 2.( 2 + 2 ) + 4.( 4 + 2 ) + 6.( 6 + 2 ) + ...... + 98.( 98 + 2 ) + 100.( 100 + 2 )

<=> S = 2.2 + 2² + 2.4 + 4² + 2.6 + 6² + .... + 2.98 + 98² + 2.100 + 100²

<=> S = ( 2² + 4² + ... + 98²  + 100² ) + ( 2.2 + 2.4 + 2.6 + .... + 2.98 + 2.100 )

<=> S = 2².( 1² + 2² + ... +49² + 50² ) + 4.( 1 + 2 + 3 + .... + 49 + 50 )

Đặt A = 1² + 2² + 3² + .... + 49² + 50² 

      B = 1 + 2 + 3 + .... + 49 + 50

=> S = 4A + 4B

A = 1² + 2² + 3² + .... + 49² + 50²

<=> A = 1.1 + 2.2 + 3.3 + .... + 49.49 + 50.50

<=> A = 1.( 2 - 1 ) + 2.( 3 - 1 ) + 3.( 4 - 1 ) + .... + 49.(50 - 1 ) + 50.( 51 - 1 )

<=> A = 1.2 - 1 + 2.3 - 2 + 3.4 - 3 + .... + 49.50 - 49 + 50.51 - 50

<=> A = ( 1.2 + 2.3 + 3.4 + .... + 49.50 + 50.51 ) - ( 1 + 2 + 3 + ... + 49 + 50 )

Đặt C = 1.2 + 2.3 + 3.4 + .... + 49.50 + 50.51

      D = 1 + 2 + 3 + .... + 49 + 50

=> A = C - D

C = 1.2 + 2.3 + 3.4 + ... + 49.50 + 50.51

<=> 3C = 1.2.3 + 2.3.3 + 3.4.3 + ..... + 49.50.3 + 50.51.3

<=> 3C = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + 4.5.( 6 - 3 ) + ..... + 49.50.( 51 - 48 ) + 50.51.( 52 - 49 )

<=> 3C = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + .... + 49.50.51 - 48.49.50 + 50.51.52 - 49.50.51

<=> 3C = 50.51.52

=> C = ( 50.51.52 ) : 3 = 44200

D = 1 + 2 + 3 + .... + 50

SSH : ( 50 - 1 ): 1 + 1 = 50 ( SH )

=> D = ( 50 + 1 ) . 50 : 2 = 1275

=> A = 44200 - 1275 = 42925

B = 1 + 2 + 3 + ... + 49 + 50 

SSH : ( 50 - 1 ) : 1 + 1 = 50 ( SH )

=> B = ( 50 +1 ) . 50 : 2 = 1275

=> S = ( 42925 + 1275 ) . 4 = 176800

Vậy S = 176800