Question

Tính tổng :

B = 1.2 + 2.3 + 3.4 + ... + 99.100

C = 1.3 +2.4 +3.5 + 4.6 + ... + 9.11 

Answer 1

B = 1.2+2.3+3.4+...+99.100

B=1.100

B=100

C=1.3+2.4+3.5+4.6+...+9.11

C=1.(2+1)+2.(3+1)+3.(4+1)+4.(5+1)+...+9.(10+1)

C=1.2+1+2.3+1+3.4+1+4.5+1+...+9.10+1

C=(1.2+2.3+3.3+4.5+...+9.10)+(1+1+1+1+..+1)

C=1.10+10

C=10+10

C=20

Answer 2

a) B = 1.2+2.3+3.4+..+99.100

=>3B=1.2.3+2.3.3+3.4.3+...+99.100.3

3B = 1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)

3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5-2.3.4+...+99.100.101-98.99.100

3B = (1.2.3+2.3.4+3.4.5+..+99.100.101) - (1.2.3+2.3.4+...+98.99.100)

3B = 99.100.101

\(B=\frac{99.100.101}{3}=333300\)

b) C = 1.3+2.4+3.5+4.6+...+9.11

C = (2-1).(2+1)+(3-1).(3+1) + (4-1).(4+1)+(5-1).(5+1)+...+(10-1).(10+1)

C = 2² - 1 + 3² - 1 + 4² - 1 + 5² - 1 +...+10² - 1

C = (2²+3²+4²+5²+...+10²) -(1+1+...+1) 

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