1)

\(\left(a\right)37+397+3997+39997\)

\(=40-3+400-3+4000-3+40000-3\)

\(=\left(40+400+4000+40000\right)-\left(3+3+3+3\right)\)

\(=44440-12=44428\)

\(\left(b\right)298+2998+29998+299998\)

\(=300-2+3000-2+30000-2+300000-2\)

\(=\left(300+3000+30000+300000\right)-\left(2+2+2+2\right)\)

\(=333300-8=333296\)

\(\left(c\right)9+99+999+9999+99999\)

\(=10-1+100-1+1000-1+10000-1+100000-1\)

\(=\left(10+100+1000+10000+100000\right)-\left(1+1+1+1+1\right)\)

\(=111110-5=111105\)

2)
\(\left(a\right)\left(2+4+6+...+2002+2004+2006\right)-\left(1+3+5+...+2001+2003+2005\right)\)

\(=\left(2-1\right)+\left(4-3\right)+\left(6-5\right)+...+\left(2002-2001\right)+\left(2004-2003\right)+\left(2006-2005\right)\)

\(=1+1+1+...+1+1+1\)( 1003 số 1 )

\(=1003\)

\(\left(b\right)88-87+86-85+84-83+...+6-5+4-3+2-1\)

\(=\left(88-87\right)+\left(86-85\right)+\left(84-83\right)+...+\left(6-5\right)+\left(4-3\right)+\left(2-1\right)\)

\(=1+1+1+...+1+1+1\)( 44 số 1 )

\(=44\)

\(\left(c\right)100-98+96-94+92-90+...+12-10+8-6+4-2\)

\(=\left(100-98\right)+\left(96-94\right)+\left(92-90\right)+...+\left(12-10\right)+\left(8-6\right)+\left(4-2\right)\)

\(=2+2+2+...+2+2+2\) ( 25 số 2 )

\(=50\)

3)

\(\left(a\right)360-357+354-351+348-345+...+312-309+306-303+300-297\)

\(=\left(360-357\right)+\left(354-351\right)+\left(348-345\right)+...+\left(312-309\right)+\left(306-303\right)+\)\(\left(300-297\right)\)

\(=3+3+3+3+3+3+3+3+3+3+3=33\)

\(\left(b\right)2006-1-2-3-4-...-47-48-49-50\)

\(=2006-\left(1+2+3+4+...+47+48+49+50\right)\)

\(=2006-\frac{\left(50+1\right)\left[\left(50-1\right)+1\right]}{2}\)

\(=2006-1275=731\)

\(\left(c\right)280-276+272-268+264-260+...+216-212+208-204+200-196\)

\(=\left(280-276\right)+\left(272-268\right)+\left(264-260\right)+...+\left(216-212\right)+\left(208-204\right)+\)\(\left(200-196\right)\)

\(=4+4+4+4+4+4+4+4+4+4+4=44\)

Cảm ơn bạn nha

$88-87+86-85+...+4-3+2-1$

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

Từ $1->88$ có số số hạng là:

$(88-1):1+1=88$(số hạng)

Số số $1$ là:

$88:2=44$(số $1$)

Vậy dãy trên có kết quả là $1\times44=44$

Ta có: \(A=1.3+2.4+3.5+4.6+...+99.101+100.102\)

\(A=1.\left(1+2\right)+2.\left(2+2\right)+3.\left(3+2\right)+4.\left(4+2\right)+....+99.\left(99+2\right)+100.\left(100+2\right)\)

\(A=\left(1^2+2^2+3^2+4^2+...+99^2+100^2\right)+\left(2+4+6+8+...+198+200\right)\)Đặt \(B=1^2+2^2+3^2+4^2+5^2+...+99^2+100^2\)

\(\Rightarrow B=\left(1^2+2^2+3^2+4^2+5^2+...+99^2+100^2\right)-2^2.\left(1^2+2^2+3^2+4^2+5^2+....+49^2+50^2\right)\)Tính dãy tổng quát \(C=1^2+2^2+3^2+4^2+5^2+...+n^2\)

\(C=1\left(0+1\right)+2\left(1+1\right)+3.\left(2+1\right)+4.\left(3+1\right)+5\left(4+1\right)+...+n\left[\left(n-1\right)+1\right]\)

\(C=\left[1.2+2.3+3.4+4.5+...+\left(n-1\right).n\right]+\left(1+2+3+4+5+....+n\right)\)

\(C=n.\left(n+1\right).\left[\left(n-1\right):3+1:2\right]=n.\left(n+1\right).\left(2n+1\right):6\)

Áp dụng vào B ta được:

\(B=100.101.201:6-4.50.51.101:6=166650\)

\(\Rightarrow A=166650+\left(200+2\right).100:2\)

\(\Rightarrow A=166650+10100=176750\)

Vậy A = 176750

Chúc bạn học tốt!!

= ( 90 - 89 ) + ( 88 - 87 ) + ( 86 - 85 )+...+ ( 2 - 1 ) 

= 1 + 1 + 1 + ... + 1 ( 45 số 1 ) 

= 45 

là -10645 nha

10645 nha chúc bạn học tốt

=10645

Câu F có lộn đề ko bạn

2008-1/2008=2007/2008

1/2-1/2009=2007/2009