ta có A = 1+(1+2)+....+(1+2+..+100) = 1 x 100 + 2 x 99 + ...+100 x 1

\(\Rightarrow\frac{A}{100.1+99.2+...+1.100}=\frac{100.1+99.2+..+1.100}{100.1+99.2+..+100.1}=1\)  

Ta có:A = 3 + 3² + 3³ + ... + 3¹⁰

          3A = 3² + 3³ + 3⁴ + .... + 3¹⁰ + 3¹¹

 3A - A = 3¹¹ - 3

      A = (3¹¹ - 3) : 2 = 88572

Ta có A = 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2 = 1/2.2 + 1/3.3 + 1/4.4 + ... + 1/100.100 < 1/4 + 1/2.3 + 1/3.4 + ... + 1/99.100                  A < 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100  = 1/4 + 1/2 - 1/100 = 3/4 - 1/100                                                                                      \(\Rightarrow\) A < 3/4 ( đpcm )       

bạn giải rõ ra được không

Ta có: \(\frac{3}{4}=\frac{1}{4}+\frac{1}{2}\)

\(\Rightarrow A=\frac{1}{2^2}+\left(\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}\right)\)

\(\Rightarrow A< \frac{1}{2^2}+\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\right)\)

\(\Rightarrow A< \frac{1}{2^2}+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(\Rightarrow A< \frac{1}{2^2}+\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(\Rightarrow A< \frac{1}{2^2}+\frac{49}{100}\)

Mà \(\frac{49}{100}< \frac{1}{2}\)

\(\Rightarrow A< \frac{3}{4}\)

~Mik cũng hok Toán 2 ney~

Có 1+(-2)+3+(-4)+...+19+(-20)

=[1+(-2)]+[3+(-4)]+....+[19+(-20)]

=(-1)+(-1)+.....+(-1)

=(-1).10

=(-10) 

     Hok tốt nha

1+(-2)+3+(-4)+...+19+(-20)

=[1+(-2)]+[3+(-4)]+...+[19+(-20)]

=-1+(-1)+...+(-1)      ( có 10 số -1)

=-1.10

=-10

hi cảm ơn

1+1-2:3x0+5-9

=1+1+0+5-9

=2+5-9

=7-9=-2

1 + 1 - 2 : 3 x 0 + 5 - 9

= 1 + 1 - 2 : 0 + 5 - 9

= 2 - 2 : 0 + 5 - 9

= 2 - 0 + 5 - 9

= 2 + 5 - 9

= - 2

1 + 1 - 2 : 3 x 0 + 5 - 9

= 1 + 1 - 2/3 x 0 + 5 - 9

= 1 + 1 - 0 + 5 - 9

= 2 + 5 - 9 

= 7 - 9

= -2

C = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... + 2002 - 2003 - 2004 + 2005 + 2006

C = 1 + ( 2 - 3 - 4 + 5 ) + ( 6 - 7 - 8 + 9 ) + ... + ( 2002 - 2003 - 2004 + 2005 ) + 2006

C = 1 + 0 + 0 + ... + 0 + 2006

C = 1 + 2006

C = 2007

C = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... + 2002 - 2003 - 2004 + 2005 + 2006

Số số hạng của C từ 1 đến 2004 : ( 2004 - 1 ) : 1 + 1 = 2004

Nhóm 4 số thành 1 cặp ta được : 2004 : 4 = 501

=> C = ( 1 + 2 - 3 - 4 ) + ( 5 + 6 - 7 - 8 ) +  ... + ( 2001 + 2002 - 2003 - 2004 ) + ( 2005 + 2006 )

C = -4 + (-4) + ... + (-4) + 4011

C = -4 . 501 + 4011

C = -2004 + 4011

C = 2007

C = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... + 2002 - 2003 - 2004 + 2005 + 2006 (Có 2006 số)

C = (1 + 2 - 3 - 4) + (5 + 6 - 7 - 8) + ... + (2001 + 2002 - 2003 - 2004) + (2005 + 2006)

C = (-4) + (-4) + ... + (-4) + 4011 (Có 501 số -4)

C = (-4) .  501 + 4011

C = (-2004) + 4011

C = 2007

Vậy C = 2007

Banh Bao Tong

a) \(M=\frac{2\times2}{1\times5}+\frac{2\times2}{5\times9}+\frac{2\times2}{9\times13}+...+\frac{2\times2}{45\times40}\)

\(M=\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+...+\frac{4}{45\times49}\)

\(M=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{45}-\frac{1}{49}\)

\(M=1-\frac{1}{49}\)

\(M=\frac{48}{49}\)

b) \(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+5+...+10}\)

=  \(\frac{2}{2\times\left(1+2\right)}+\frac{2}{2\times\left(1+2+3\right)}+...+\frac{2}{2\times\left(1+2+3+...+10\right)}\)

\(=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{110}\)

\(=\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{10\times11}\)

\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(=2\times\frac{9}{22}\)

\(=\frac{9}{11}\)

Mình trả lời câu a nha  M= 4/1*5+4/5*9+4/9*13+...+4/45*49   M=1-1/5+1/5-1/9+1/9-1/13+...+1/45-1/49    M=1-1/49=48/49

mình na

\(a,\frac{62}{7}:x=\frac{29}{9}:\frac{3}{56}\)

\(\frac{62}{7}:x=\frac{1624}{27}\)

\(x=\frac{62}{7}:\frac{1624}{27}=\frac{837}{5684}\)

\(b,\frac{1}{5}:x=\frac{1}{5}-\frac{1}{7}\)

\(\frac{1}{5}:x=\frac{2}{35}\)

\(x=\frac{1}{5}:\frac{2}{35}=\frac{7}{2}\)

\(c,\frac{2}{3}.x-\frac{4}{7}=\frac{1}{7}\)

\(\frac{2}{3}.x=\frac{1}{7}+\frac{4}{7}=\frac{5}{7}\)

\(x=\frac{5}{7}:\frac{2}{3}=\frac{15}{14}\)

\(d,\frac{2}{7}-\frac{8}{9}.x=\frac{2}{3}\)

\(\frac{8}{9}.x=\frac{2}{7}-\frac{2}{3}=-\frac{8}{21}\)

\(x=-\frac{8}{21}:\frac{8}{9}=-\frac{3}{7}\)

\(e,\frac{4}{7}+\frac{5}{9}:x=\frac{1}{5}\)

\(\frac{5}{9}:x=\frac{1}{5}-\frac{4}{7}=-\frac{13}{35}\)

\(x=\frac{5}{9}:-\frac{13}{35}=\frac{175}{117}\)

\(i,\frac{2}{5}-\frac{2}{5}.x=\frac{2}{5}\)

\(\frac{2}{5}.\left(1-x\right)=\frac{2}{5}\)

\(1-x=\frac{2}{5}:\frac{2}{5}=1\)

\(x=1-1=0\)

\(g,\frac{2}{3}+\frac{1}{3}:x=-1\)

\(\frac{1}{3}:x=-1-\frac{2}{3}=-\frac{5}{3}\)

\(x=\frac{1}{3}:-\frac{5}{3}=-\frac{1}{5}\)

học tốt nha