Question

Consider the series 1/8+1/16+1/32+1/64+1/128+... Which expression defines Sn?

Answer 1

Answer:

Answer is Option B.

That is the nth term of the sequence.

1/8 + 1/16 + 1/32....

You notice that all the numerators are the same. Which is (1).

so we have to both about getting the nth term of the denominator

Since all the denominator are divisible by 2... and Your intuition should tell you that they'd multiples of 2

So Lets go with 2^n

2^n

let n be all Integers

let take 1,2,3

2¹ = 2

2² = 4

2³ = 8

Now Observe that

If you multiply all these by 4... We will have all the values of the denominator

which are 4,16,32

So thats our nth term

1/4(2^n)

as n approaches positive Infinity.