không biết giải

2001 

____

1991

1/1*2+1/2*3+1/3*4+1/4*5+...1/99+100

= 1/1x2 + 1/2x3 + 1/3x4 ...... +1/9x10

= 1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10

=1-1/10=9/10

đặt A=1/1 x 1/2 + 1/2 x 1/3 + 1/3 + 1/4 + .......... + 1/9 x 1/10

\(A=\frac{1}{1}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+...+\frac{1}{9}\cdot\frac{1}{10}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{9}{10}\)

đặt B=2/1 x 2 + 2/2 x 3 + 2/3 x4 + .............. + 2/98 x 99 + 2/99 x 100

\(B=2\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)\)

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

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

\(=2\times\frac{99}{100}\)

\(=\frac{99}{50}\)

\(A=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}........\frac{2010}{2009}=\frac{3.4.5...2010}{2.3.4....2009}=\frac{2010}{2}=1005\)

\(B=\frac{1.2.3......99}{1.2.3.4.....100}=\frac{1}{100}\)

vì tử của tất cả các số là 1-1 mà 1-1=0

suy ra:=0+0+0+...+0 (100 số 0)

Suy ra:=0

vậy (1-1/1+2).(1-1/1+2+3).....(1-1/1+2+3+...+99+100)=0

\(\left(1+\dfrac{1}{2}\right)\times\left(1+\dfrac{1}{3}\right)\times\left(1+\dfrac{1}{4}\right)\times....\times\left(1+\dfrac{1}{98}\right)\times\left(1+\dfrac{1}{99}\right)\)

\(=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times...\times\dfrac{99}{98}\times\dfrac{100}{99}\)

\(=\dfrac{1\times100}{2\times1}\)

\(=\dfrac{100}{2}\\ =50\)

50

\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)......\left(\dfrac{1}{99}-1\right)\left(\dfrac{1}{100}-1\right)\)

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

\(=\dfrac{1}{100}\) ( do có 100 số hạng nên tích ra 1 số dương nhé ! ( chẵn mà )

Nhi có 10 viên bi,Nhi cho Oanh 5 viên bi.Hỏi Nhi còn lại bao nhiêu viên bi?

1+9=?

G = 1.2 + 1 + 2.3 + 1 + 3.4 + 1 + ... + 99.100 + 1

= 1.2 + 2.3 + 3.4 + ... + 99.100 + 99

⇒ 3G = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3 + 99.3

= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)

= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 - ... - 98.99.100 + 99.100.101 + 297

= 99.100.101 + 297

= 1000197

⇒ G = 1000197 : 3

= 333399

M = \(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+...+\dfrac{1}{99x100}\)

M = \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

M = \(1-\dfrac{1}{100}\)

M = \(\dfrac{99}{100}\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

học tốt nha

=99/100

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

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

\(=\frac{1}{1}-\frac{1}{100}\)

\(=\frac{100}{100}-\frac{1}{100}\)

\(=\)\(\frac{99}{100}\)