\(S=\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1.2+2.3+3.4+....+98.99}\)

\(=\frac{1+\frac{2.3}{2}+\frac{3.4}{2}+....+\frac{98.99}{2}}{1.2+2.3+3.4+....+98.99}\)

\(=\frac{\frac{1}{2}\left(1.2+2.3+3.4+....+98.99\right)}{1.2+2.3+3.4+....+98.99}\)

\(=\frac{1}{2}\)

sao toàn thấy frac, left và right ko vậy?

A=1.2+2.3+3.4+.......+99.100
Nhân cả 2 vế với 3, ta được:
3A=1.2.3+ 2.3.3+ 3.4.3+ 4.5.3+...... 99.100.3
= 1.2.3 + 2.3(4-1) + 3.4.(5-2) +...+ 99.100.(101-98)
= 1.2.3 + 2.3.4 -1.2.3 + 3.4.5-2.3.4 +...+ 99.100.101-98.99.100= 99.100.101
=> A = (99.100.101)/3
A = 333300

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

5S = (1.2.3.4+2.3.4.5+3.4.5.6+ ... + 97.98.99.100).5

5S = 1.2.3.4.(5-0) + 2.3.4.5.(6-1)+ 3.4.5.6(7-2)+......+ 97.98.99.100.(101-96)

 5S = (1.2.3.4.5 + 2.3.4.5.6 + 3.4.5.6.7 + ....+ 97.98.99.100.101) - (0.1.2.3.4 + 1.2.3.4.5 + 2.3.4.5.6+.....+96.97.98.99.100)

 5S = 97.98.99.100.101

 S= 97.98.99.100.101/5

 S=1901009880

S=1*2*3*4+2*3*4*5+....+97*98*99*100

5S=1.2.3.4.5+2.3.4.5.5+...+97.98.99.100.5

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

5S=1.2.3.4.5-0.1.2.3.4+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99.100

5S=(1.2.3.4.5+2.3.4.5.6+...+97.98.99.100.101)-(0.1.2.3.4+1.2.3.4.5+...+96.97.98.99.100)

5S=97.98.99.100.101

S=9505049400:5=1901009880.

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

5S = (1.2.3.4+2.3.4.5+3.4.5.6+ ... + 97.98.99.100).5

5S = 1.2.3.4.(5-0) + 2.3.4.5.(6-1)+ 3.4.5.6(7-2)+......+ 97.98.99.100.(101-96)

5S = (1.2.3.4.5 + 2.3.4.5.6 + 3.4.5.6.7 + ....+ 97.98.99.100.101) - (0.1.2.3.4 + 1.2.3.4.5 + 2.3.4.5.6+.....+96.97.98.99.100)

5S = 97.98.99.100.101

S= 97.98.99.100.101/5

S=1901009880 

2S=1x2x3+2x3x3+3x4x3+...+98x99x3+99x100x3

3S=1x2x3+2x3x(4-1)+3x4x(5-2)+...+98x99x(100-97)+99x100x(101-98)

3S=1x2x3-1x2x3+2x3x4-2x3x4+3x4x5-...-97x98x99+98x99x100-98x99x100+99x100x101=99x100x101

S=33x100x101=333300

3xS = 1x 2x 3 + 2x3x3 + 3x4x3 + ...+ 98x99x3 + 99x100x3

= 1x2x3 + 2x3x(4-1) + 3x4x(5-2) +...+98x99x(100-97) + 99x100x(101-98)

= 1x2x3 -1x2x3 + 2x4x4 -2x3x4 + 3x4x5 +...- 97x98x99 +98x99x100  -98x99x199 + 99x100x101

= 99x100x101 = 999900 

=> S = 999900 : 3 =333300

=333300 nha

mong bn k mik

khong ro dau bai ra lam sao

lại gặp bài nữa ko có câu hỏi!chán quá

S=1-3+3^2-3^3+.....+3^98-3^99    (1)

3S=3-3^2+3^3+.......+3^99-3^100    (2)

Từ (1) và (2) ta có:

4S=1-3^100

Do đó S chia hết cho -20 => 4S chia hết cho -20 => 4S chia hết cho 4 => 1-3^100 chia hết cho 4

Vậy 3^100 chia 4 dư 1

Xin hãy giúp mình

a,=3/2*4/3*....100/99

=3*4*5*....*100/2*3*...*99

=100/2=50

b, nhân lên băng:

1*2*3*...*99/2*3*...*100=1/100

a)số các số hạng trong S là:

(98-2):2+1=49(số)

Tổng S là:

(2+98).45:2=2250

b) số các số hạng là:

(99-1):2+1=50(số)

tổng S là:

(99+1).50:2=2500

S:2+4+6+8+...+98=2450

S:1+3+5+7+...+99=2500

S=2+4+6+8+...+98

S=((98-2):2+1)x((98+2):2)

S=49x50

S=2450