Question

tìm A biết A=1.2+2.3+3.4+4.5+...+99.100+100.101

Answer 1

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Answer 2

A = 1.2 + 2.3 + 3.4 + ... + 99.100 + 100.101

⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3 + 100.101.3

= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98) + 100.101.(102 - 99)

= 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + 3.4.5 + ... - 98.99.100 + 99.100.101 - 99.100.101 + 100.101.102

= 100.101.102

= 1030200

⇒ A = 1030200 : 3

= 343400