Question

Giúp mình làm bài này với mình đang cần gấp😢😢😢

Answer 1

A                   =      \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\)+ \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\) + \(\dfrac{1}{64}\)+......+\(\dfrac{1}{1024}\)

A \(\times\)2           = 1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)+\(\dfrac{1}{64}\)+...+\(\dfrac{1}{512}\)

A\(\times\)2 - A     =   1 - \(\dfrac{1}{1024}\)

A               = \(\dfrac{1023}{1024}\)

Answer 2

B = \(\dfrac{1}{1\times2}\)+\(\dfrac{1}{2\times3}\)+\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{4\times5}\)+...+\(\dfrac{1}{98\times99}\)+\(\dfrac{1}{99\times100}\)

B = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)+ \(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{5}\)+...+\(\dfrac{1}{98}\)-\(\dfrac{1}{99}\)+\(\dfrac{1}{99}\)-\(\dfrac{1}{100}\)

B = 1 - \(\dfrac{1}{100}\)

B = \(\dfrac{99}{100}\)

Answer 3

C= \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\)+ \(\dfrac{1}{20}\)+ \(\dfrac{1}{30}\)+\(\dfrac{1}{42}\)+...+\(\dfrac{1}{90}\)+\(\dfrac{1}{110}\)

C = \(\dfrac{1}{2\times3}\) +\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+...+\(\dfrac{1}{9\times10}\)+\(\dfrac{1}{10\times11}\)

C = \(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+...+\(\dfrac{1}{9}\)-\(\dfrac{1}{10}\)+\(\dfrac{1}{10}\)-\(\dfrac{1}{11}\)

C = \(\dfrac{1}{2}\) - \(\dfrac{1}{11}\)

C = \(\dfrac{9}{22}\)