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\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\left(\dfrac{1}{2}-\dfrac{1}{2}\right)-\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-...-\left(\dfrac{1}{99}-\dfrac{1}{99}\right)-\dfrac{1}{100}\\ =1-0-0-...-0-\dfrac{1}{100}\\ =1-\dfrac{1}{100}\\ =\dfrac{99}{100}\)
1/1.2 + 1/2.3 + .... + 1/99.100
= 1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100
= 1 - ( 1/2 - 1/2 ) - ( 1/3 - 1/3 ) - ..... - ( 1/99 - 1/99 ) - 1/100
= 1 - 0 - 0 - .... - 1/100
= 1 - 1/100
= 99/100
![](https://rs.olm.vn/images/avt/0.png?1311)
Số số hạng:
(100 - 2) : 2 + 1 = 50 (số hạng)
Tổng trên bằng:
(100 + 2) . 50 : 2 = 2 550
Số số hạng là :
(100-2):2 +1=50 (số)
Tổng đó là :
(2+100).50 :2=2550
Vậy 2+4+6+8+.......+98+100=2550
![](https://rs.olm.vn/images/avt/0.png?1311)
=(1 - 2 - 3 + 4) + (5 - 6 - 7 + 8) + ......+ ( 21 - 22 - 23 + 24)
= 0+0+0+......+0
=0 nha
1-2-3+4+5-6-7+8+.....+21-22-23+14
=(1-2-3+4)+(5-6-7+8)+....+(21-22-23+24)
=0+0+...+0
=0
![](https://rs.olm.vn/images/avt/0.png?1311)
A= 2.2.2+ 2.2.2.2.2+ 2.2.2.2.2.2.2+ ..........+ 2.2.2.2.2.2.2.2..2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2.2..2.2= tu lam
Cách 1 :
A = 2.4 + 4.6 + 6.8 + ... + 98.100
6.A = 2.4.6 + 4.6.6 + 6.8.6 +...+ 98.100.6
6.A = 2.4.6 + 4.6.( 8 - 2 ) + 6.8.( 10 - 4 ) +...+ 98.100.( 102 - 96 )
6.A = 2.4.6 + 4.6.8 - 2.4.6 + 6.8.10 - 4.6.8 + ... + 98.100.102 - 96.98.100
6.A = ( 2.4.6 - 2.4.6 ) + ( 4.6.8 - 4.6.8 ) + ( 6.8.10 - 6.8.10 ) + ... + ( 96.98.100 - 96.98.100 ) + 98.100.102
6.A = 98.100.102
A = 98.100.102 : 6 = 166600
Cách 2 ( mik chịu )
1553
khó quá ! ai làm đc mk bái làm sư phụ luôn