Question

Tính nhanh:

P=\(\frac{12}{1.4.7}\)+ \(\frac{12}{4.7.10}\)+\(\frac{12}{7.10.13}\)+....+ \(\frac{12}{54.57.60}\)

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Answer 1

\(P=\frac{12}{1.4.7}+\frac{12}{4.7.10}+\frac{12}{7.10.13}+...+\frac{12}{54.57.60}\)

\(P=4.\left(\frac{3}{1.4.7}+\frac{3}{4.7.10}+\frac{3}{7.10.13}+...+\frac{3}{54.57.60}\right)\)

\(P=4\left(\frac{1}{1.4}-\frac{1}{4.7}+\frac{1}{4.7}-\frac{1}{7.10}+\frac{1}{7.10}+...+\frac{1}{54.57}-\frac{1}{57.60}\right)\)

\(P=4.\left(\frac{1}{4}-\frac{1}{3420}\right)\)

\(P=4.\frac{427}{1710}\)

\(P=\frac{854}{855}\)