Question

The series 2+ 4 +6+8.... Is
(a) Convergent
(c) unbounded
(b) Divergent
(d) none of these​

Answer 1

Answer:

(B) divergent

Step-by-step explanation:

correct answer

Answer 2

The series 2 + 4 + 6 + 8 . . . . is Divergent

Given :

The series 2 + 4 + 6 + 8 . . . .

To find :

The series 2 + 4 + 6 + 8 . . . . is

(a) Convergent

(b) Divergent

(c) unbounded

(d) none of these

Concept :

$\boxed{ \: \: \displaystyle \sf If \: \sum \:a_n \: converges \: then \: \lim_{n \to \infty } \: a_n = 0 \: \: }$

Solution :

Step 1 of 2 :

Find nth term of the sequence

Here the given series is 2 + 4 + 6 + 8 . . . .

Let nth term of the series = aₙ

Then aₙ = 2n

Step 2 of 2 :

Test the convergence of the series

$\displaystyle \sf\lim_{n \to \infty } \: a_n$

$\displaystyle \sf = \lim_{n \to \infty } \: 2n$

$\displaystyle \sf = \infty \ne \: 0$

We know that

$\displaystyle \sf If \: \sum \:a_n \: converges \: then \: \lim_{n \to \infty } \: a_n = 0$

Therefore the series is divergent

Hence the correct option is (b) Divergent