Question

Given series \[1 + 0.5 + 0.25 + 0.125...\] is an example of
A.finite geometric progression
B.infinite geometric series
C.finite geometric sequence
D.infinite geometric progression

Answer 1

Hint: In the given question, we have been asked out of the given four options, to what category does \[1 + 0.5 + 0.25 + 0.125...\] belong to. Clearly, this is a geometric one with first term as one and common ratio as half.

Complete step-by-step answer:
The given series is \[1 + 0.5 + 0.25 + 0.125...\]
It is a geometric expression clearly, with
First term, \[a = 1\], and
Common ratio, \[r = 0.5\]
Now, this expression is an infinite one because no endpoint has been given to it.
A geometric sequence or a geometric progression (both terms mean the same thing) is a sequence of numbers with each term found by multiplying the previous one with the common ratio. Whereas, a geometric series is the sum of numbers in a geometric progression.
Hence, this expression is an infinite geometric series.
Thus, the correct option is B.

Note: So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we write the formula which connects the two things. The only thing we need to pay attention to is when is the expression a geometric one and when is it an arithmetic one.