Question

[Cô bé bánh bèo]

Bài 1 : tính 

B = 1.2+2.3+3.4+....+50

C = 1²+2²+3² +...+ 50²

Giúp mình nha mấy bạn 

Answer 1

[Nguyễn Huy Tú]

\(B=1.2+2.3+3.4+...+49.50\)

\(\Rightarrow3B=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)

\(\Rightarrow3B=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)

\(\Rightarrow3B=49.50.51\)

\(\Rightarrow B=\frac{49.50.51}{3}\)

Answer 2

[Ngô Tấn Đạt]

B=\(1.2+2.3+....+49.50\\ \Rightarrow3B=1.2.\left(3-0\right)+2.3.\left(4-1\right)+.....+49.50.\left(51-48\right)\)

\(\Rightarrow3B=1.2.3-0.1.2+2.3.4-1.2.3.+.....+49.50.51-48.49.50\\ \Rightarrow3B=49.50.51\\ \Rightarrow3B=124950\\ \Rightarrow B=41650\)

C=\(1^2+2^2+3^2+....+50^2\\ =1.1+2.2+3.3+.....+50.50\\ =1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+....+50\left(51-1\right)\\ \)

\(=\left(1.2+2.3+3.4+.....+50.51\right)-\left(1+2+3+....+50\right)\)

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