Tính bằng cách thuận tiện nhất:

\(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{{27}} + \frac{1}{{81}} + \frac{1}{{243}} + \frac{1}{{729}}\)

Tính:

\(\frac{2}{{1 \times 3}} + \frac{2}{{3 \times 5}} + \frac{2}{{5 \times 7}} + ..... + \frac{2}{{97 \times 99}} = ...\)

Tìm x:

\(\frac{1}{{11 \times 16}} + \frac{1}{{16 \times 21}} + \frac{1}{{21 \times 26}} + \ldots + \frac{1}{{x \times (x + 5)}} = \frac{7}{{506}}\)

Tính tổng A biết:

\(A = 1 + \frac{1}{3} + \frac{1}{6} + \frac{1}{{10}} + \frac{1}{{15}} + \frac{1}{{21}} + \frac{1}{{28}} + \frac{1}{{36}} + \frac{1}{{45}} + ......\)

Tính:

a) \(\frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + ..... + \frac{1}{{19 \times 20}} = ......\)

b) \(\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + ..... + \frac{1}{{72}} + \frac{1}{{90}} = ......\)

Tìm số tự nhiên x:

\(\frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + ..... + \frac{1}{{x \times (x + 1)}} = \frac{{2017}}{{2018}}\)

Tìm x: \((\frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + ... + \frac{1}{{90}}):x = \frac{9}{{20}}\)

Tính: \(\frac{1}{8} + \frac{1}{{24}} + \frac{1}{{48}} + \frac{1}{{80}} + \frac{1}{{120}} = ...\)