Question

Cho P=1/1×3+13/3×5+33/5×7+...+193/13×15.Hỏi tổng P có bao nhiêu số hạng và so sánh P với 6.

Answer 1

P = \(\frac{1}{3}\)+ \(\frac{13}{15}\)+\(\frac{33}{35}\)+...+\(\frac{193}{195}\)(7 số hạng)

P = (\(\frac{3}{3}\)-\(\frac{2}{3}\)) + ( \(\frac{15}{15}\)-\(\frac{2}{15}\) ) + ... + (\(\frac{195}{195}\)-\(\frac{2}{195}\) )

P = (1+1+1+..+1) -(\(\frac{2}{3}\)+\(\frac{2}{15}\)+\(\frac{2}{35}\)+...+\(\frac{2}{195}\))

P = 7 - (\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+...+\(\frac{2}{13.15}\))

P = 7 - (1 - \(\frac{1}{3}\)+ \(\frac{1}{3}\)-\(\frac{1}{5}\)+...+\(\frac{1}{13}\)-\(\frac{1}{15}\))

P = 7 - (1 - \(\frac{1}{15}\))

P = 7 - 1 +\(\frac{1}{15}\)

P = 6 + \(\frac{1}{15}\)

=> P > 6