Đặt A=1.2.3.4+2.3.4.5+...+97.98.99.100

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101

4A=98.99.100.101

A=98.99.100.101/4 

5A=(5-0).1.2.3.4+(6-1).2.3.4.5+...+(101-96).97.98.99.100

5A=1.2.3.4.5-0+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100

5A=97.98.99.100.101=9505049400

A=1901009880

Nguyen Quang Trung sai

B=1901009880

\(\text{Ta có S=1.2.3.4+2.3.4.5+3.4.5.6+...+97.98.99.100 }\)
\(\text{\Rightarrow5S=(5-0).1.2.3.4+(6-1).2.3.4.5+...+(101- 96).97.98.99.100 }\)
\(\text{\Rightarrow5S=1.2.3.4.5-0+2.3.4.5.6- 1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100 }\)

5S=97.98.99.100.101

5S  =9505049400 

Đặt S= 1.2.3.4+2.3.4.5.6+3.4.5.6+...+97.98.99.100
5S=(5-0).1.2.3.4+(6-1)+2.3.4.5+...+(101-96).97.98.99.100
5S=1.2.3.4.5-0+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100
5S=97.98.99.100.101=9505049400
S=1901009880
k nha      công chúa chipu

  Giáng Long Tôn Giả làm sai rồi.

\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100} \)

\(=\frac{1}{3}.\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)=\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)=\frac{1}{18}-\frac{1}{6.970200}\)

\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{97.98.99.100}\)

=\(\frac{1}{3}\cdot\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{97.98.99.100}\right)\)

=\(\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{4.5.6}+...+\frac{1}{97.98.99}-\frac{1}{98.99.100}\right)\)

=\(\frac{1}{3}.\left(\frac{1}{1.2.3}-\frac{1}{98.99.100}\right)\)

=\(\frac{1}{3}.\left(\frac{1}{6}-\frac{1}{970200}\right)\)

=\(\frac{1}{18}-\frac{1}{5821200}\)

5P=(5-0).1.2.3.4+(6-1).2.3.4.5+...+(101-96).97.98.99.100

5P=1.2.3.4.5-0+2.3.4.5.6-1.2.3.4.5+....+97.98.99.100.101-96.97.98.99.100

5P=97.98.99.100.101

5P=9505049400

S=1901009880

P = 1.2.3.4 + 2.3.4.5 + 3.4.5.6 + 4.5.6.7 + .. + 97.98.99.100

4P = ( 1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 + .. + 98.99.100) 4

4P = 1.2.3.(4-0) + 2.3.4(5-1) + 3.4.5(6-2) + 4.5.6(7-3) + 98.99.100(101-97)

4P = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + 4.5.6.7 - 3.4.5.6 + .. 98.99.100.101 - 97.98.99.100

4P = 98.99.100.101

4P= 98.99.100.101/4

Nếu thấy đúng thì tích mk nha

cách làm của tui đúng nhất nhưng ko bít có giống cách ai ko

đặt S=1.2.3.4+2.3.4.5+3.4.5.6+...+97.98.99.100

5S=(5-0).1.2.3.4+(6-1).2.3.4.5+...+(101-96).97.98.99.100

5S=1.2.3.4.5-0+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100

5S=97.98.99.100.101=9505049400

S=1901009880

1.2.3.4+2.3.4.5+3.4.5.6+...+97.98.99.100

4S=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100). 4

4S=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4S=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...98.99.100.101-97.98.99.100

4S=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98+99.100+101

4S=98.99.100.101

Vậy S = 98.99.100.101/4 = 24497550

1.2.3.4+2.3.4.5+3.4.5.6+...+97.98.99.100

4S=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100) 4

4S=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4S=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...98.99.100.101-97.98.99.100

4S=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98+99.100+101

4S=98.99.100.101

Vậy S=98.99.100.101/4

Giups mk với...

chờ tối nha chớ giờ giải là khỏi đi học lun

bạn vào đây nè: http://olm.vn/hoi-dap/question/601925.html

Đặt \(A=1.2.3.4+2.3.4.5+...+97.98.99.100\)

\(5A=1.2.3.4.5+2.3.4.5.5+...+97.98.99.100.5\)

\(5A=1.2.3.4.5+2.3.4.5.\left(6-1\right)+...+97.98.99.100.\left(101-96\right)\)

\(5A=1.2.3.4.5+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100\)

\(5A=97.98.99.100.101\)

\(A=\frac{97.98.99.100.101}{5}=1901009880\)