Question

cho 

a=1.2+2.3+3.4+4.5+....+98.99

b=1²+2³+3²+....+98²

 chứng minh rằng a-b chia hết cho 4851

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Answer 1

A = 1.2 + 2.3 + 3.4 + ... + 98.99

A = 1.(1 + 1) + 2.(2 + 1) + 3.(3 + 1) + ... + 98.(98 + 1)

A = 1² + 1 + 2² + 2 + 3² + 3 + ... + 98².98

A = (1² + 2² + 3² + ... + 98²) + (1 + 2 + 3 + ... + 98)

A = (1² + 2² + 3² + ... + 98²) + 4851               (1)

B = 1² + 2² + 3² + ... + 98²              (2)

(1)(2) => A - B = 4851 ⋮ 4851

Answer 2

ta có: B = 1²  + 2² + 3² +...+98² = 1.1 +2.2+3.3+...+98.98

=> A-B = (1.2+2.3+3.4+4.5+...+98.99) - (1.1+2.2+3.3+...+98.98)

A-B = (1.2-1.1) + (2.3-2.2) + (3.4-3.3) + (4.5-4.4) + ...+ (98.99-98.98)

A-B = 1.(2-1) + 2.(3-2) +3.(4-3) + 4.(5-4) + ...+ 98.(99-98)

A-B = 1 +2+3+4+...+98

A-B = (1+98).98:2

A -B = 4851 chia hết cho 4851