Find the value of 3 over 4 minus 9 over 8 plus dot dot dot plus the quotient of the product of negative 1 raised to the n plus 1 power and 3 to the nth power and the quantity 2 raised to the n...

Question

Find the value of 

A
B
C
D	The value of the series is not a finite number

Answer 1

a_n = (-1)ⁿ⁺¹3ⁿ/2ⁿ⁺¹ = (-1)ⁿ⁺¹b_n

Using the Alternating Series Test, b_n is not decreasing

lim b_n = lim 3ⁿ/2ⁿ⁺¹ = (1/2) lim (3/2)ⁿ = ∞ ≠ 0

n→∞ n→∞ n→∞

The answer is D) The value of the series is not a finite number