S = ( -1 ) + 2 + ( -3 ) + 4 + ( -5 ) + 6 + ... + ( - 99 ) + 100

S = [ ( -1 ) + 2 ] + [ ( -3 ) + 4 ] + [ ( -5 ) + 6 ] + ... + [ ( - 99 ) + 100 ]

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

S = 1 x 50

S = 50

1+2-3-4+5+6-7-8+............-99-100+101+102

=1+(2-3-4+5)+(6-7-8+9)+...............+(98-99-100+101)+102

=1+0+0+..............+0+102

=103

neu ai lam ho se k cho

A=1-2+3-4+5-6+.....+99-100+101? 
Giải 
A=1-2+3-4+5-6+.....+99-100+101. 
Ta viết lại tổng như sau: 
A = 101 - 100 + 99 - 98 + ... + 5 - 4 + 3 - 2 + 1 
A = 1 + 1 + ... + 1 + 1 + 1 
Số phép trừ trong dãy tính là: 
( 101 - 1 ) : 2 = 50 ( phép trừ ) 
Kết quả dãy số là: 
1 x 50 + 1 = 51 
Vậy: 
A=1-2+3-4+5-6+.....+99-100+101. 
A= 51

\(A=1\times3+2\times4+3\times5+4\times6+...+97\times99+98\times100\)

\(B=1\times3+3\times5+...+97\times99\)

\(6\times B=1\times3\times\left(5+1\right)+3\times5\times\left(7-1\right)+5\times7\times\left(9-3\right)+...+97\times99\times\left(101-95\right)\)

\(=1\times3+1\times3\times5+3\times5\times7-1\times3\times5+...+97\times99\times101-95\times97\times99\)

\(=1\times3+97\times99\times101\)

\(B=161651\)

\(C=2\times4+4\times6+...+98\times100\)

\(6\times C=2\times4\times6+4\times6\times\left(8-2\right)+...+98\times100\times\left(102-96\right)\)

\(=2\times4\times6+4\times6\times8-2\times4\times6+...+98\times100\times102-96\times98\times100\)

\(=98\times100\times102\)

\(C=166600\)

\(A=B+C=161651+166600=328251\)

$A=1\times 3+2\times 4+3\times 5+4\times 6+...+97\times 99+98\times 100$

$B=1\times 3+3\times 5+...+97\times 99$

$6\times B=1\times 3\times \left(5+1\right)+3\times 5\times \left(7-1\right)+5\times 7\times \left(9-3\right)+...+97\times 99\times \left(101-95\right)$

$=1\times 3+1\times 3\times 5+3\times 5\times 7-1\times 3\times 5+...+97\times 99\times 101-95\times 97\times 99$

$=1\times 3+97\times 99\times 101$

$B=161651$

$C=2\times 4+4\times 6+...+98\times 100$

$6\times C=2\times 4\times 6+4\times 6\times \left(8-2\right)+...+98\times 100\times \left(102-96\right)$

$=2\times 4\times 6+4\times 6\times 8-2\times 4\times 6+...+98\times 100\times 102-96\times 98\times 100$

$=98\times 100\times 102$

$C=166600$

$A=B+C=161651+166600=328251$

 1+2-3-4+5+6-7-8+...+97+98-99-100
=(1+2-3-4)+(5+6-7+8)+...+(97+98-99-100)
=(-4)+(-4)+...+(-4)(25 số -4)
=(-4).25=-100

=1+(2-3-4+5)+(6-7-8+9)+...+(98-99-100+101)-101

=1+0+0+...+0-101

=1-101

=-100

Nhờ mọi người giúp mình với

1 nhé bạn

1-2-3-4+5-6-7-8+9-10-11-12+...+97-98-99-100

=(1-2-3-4)+(5-6-7-8-)+(9-10-11-12)+....+(97-98-99-100)

=(-8)+(-16)+(-24)+.....+(-200)

=(-8).(1+2+3+4+.....+25)

=(-8).325

=(-2600)

thank!

Đặt \(A=5+5^2+5^3+....+5^{199}+5^{200}\)

\(\Leftrightarrow5A=5\left(5+5^2+5^3+....+5^{199}+5^{200}\right)\)

\(\Leftrightarrow5A=5^2+5^3+5^4+....+5^{200}+5^{201}\)

\(\Leftrightarrow5A-A=\left(5^2+5^3+5^4+....+5^{200}+5^{201}\right)-\left(5+5^2+5^3+....+5^{199}+5^{200}\right)\)

\(\Leftrightarrow4A=5^{201}-5\)

\(\Leftrightarrow A=\frac{5^{201}-5}{4}\)

<=> SSH:( 100 - 1 ) : 1 + 1 = 100

=> Tổng ( 100 + 1 ) . 100 : 2 = 5050

Vậy tổng đó bằng 5050