Question

1*2+2*3+3*4+...+68*69

Answer 1

    S=1.2+2.3+3.4+...+68.69

⇒ 3S= 1.2.3+2.3.3+3.4.3+...+68.69.3

    3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+68.69.(70-67)

    3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+68.69.70-67.68.69

    3S=68.69.70

⇒ S=\(\dfrac{68.69.70}{3}\)=328440

Answer 2

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Answer 3

S=1.2+2.3+3.4+...+68.69

 3S= 1.2.3+2.3.3+3.4.3+...+68.69.3

 3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+68.69.(70-67)

 3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+68.69.70-67.68.69

 3S=68.69.70

 S=(68.69.70):3

 

 

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