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H

hangxiti12

a. A= 1.3 + 2.4 + 3.5 +....+ 98.100
= 1(2+1) + 2.(3+1) + 3.(4+1) +...+ 98(99+1)
= 1.2 + 1 + 2.3 + 2 + 3.4 + 3+....+ 98.99 +98
= (1.2 + 2.3 + 3.4+....98.99) + (1+2+3+....+98)
=323400 + 4851=328251
 
H

hangxiti12

b. B = 1.2.3 + 2.3.4 +....+ 48.49.50
[TEX]\Rightarrow[/TEX]4B= 1.2.3.4 + 2.3.4.4 +.....+48.49.50.4
=1.2.3.4 + 2.3.4.(5-1) +.....+48.49.50.(51-47)
=1.2.3.4 + 2.3.4.5 - 1.2.3.4 +.....+ 48.49.50.51 - 47.48.49.50
=48.49.50.51= 1499400
 
K

khaiproqn81

$A=1.3+2.4+3.5+...+97.99+98.100 \\ A= 2^2-1+3^2-1+...+99^2-1=1^2+2^2+3^2+...+99^2-99 \\ A=\dfrac{99.100.99}{6}-99=328251$

Mình giải ngắn gọn vầy thôi
 
K

khaiproqn81

$B=1.2.3+2.3.4+3.4.5+...+48.49.50 \\ 4B=1.2.3.4+2.3.4.4+3.4.5.4+...+48.49.50.4\\ 4B=1.2.3(4-0)+2.3.4(5-1)+...+48.49.50(51-47) \\ 4B=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4 +...+48.49.50.51-48.48.49.50 = 48.49.50.51 \\ \rightarrow B=\dfrac{48.49.50.51}{4} = 1499400$
 
Last edited by a moderator:
B

buivanbao123

a. A= 1.3 + 2.4 + 3.5 +....+ 98.100
A = (1.2 + 2.3 + 3.4+....98.99) + (1+2+3+....+98)
A=$\dfrac{98.99.100}{3}+\dfrac{98.99}{2}$
A=323400+4851=328251
 
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