Explain how many terms are there in series and find sum

2 + 2(0.1) + 2(0.1)² + . . . + 2(0.1)²⁵

Find and explain sum of series

3 + 3/2 + 3/4 + 3/8 + . . . + 3/2¹⁰

Find sum of series. What values of the variable does the series converge to this sum?

y y² + y³ y⁴ +. . .

2 4z + 8z² 16z³ + . . .