Find the sum of the following series:

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Find the sum of the following series: (1)

2 + 6 + 18 + 54 + \dots

to 8 terms (2)

5 + 10 + 20 + 40 + \dots

to 10 terms (3)

12 + 6 + 3 + 1.5 + \dots

to 10 terms (4)

\sqrt{7} + 7 + 7\sqrt{7} + 49 + \dots

to 12 terms (5)

6 - 3 + 1\frac{1}{2} - \frac{3}{4} + \dots

to 15 terms (6)

1 - \frac{1}{\sqrt{2}} + \frac{1}{2} - \frac{1}{2\sqrt{2}} + \dots

to 20 terms