Find the numerical value of by using the sum formulas.
A)44
B)6
C)228
D)229
E)48

Question

Find the numerical value of  by using the sum formulas. ​
A)44 
B)6 
C)228 
D)229 
E)48

Quizplus · Accepted Answer

First, we need to convert the hexadecimal number to decimal.

11eb0d3b_9898_1fe8_9790_974aff8f78f8_TB1243_11

= 11eb0d3b98981fe89790974aff8f78f8_TB1243_11   (Take away underscores)

= (1 x 16^44) + (14 x 16^43) + (11 x 16^42) + ... + (4 x 16^2) + (3 x 16^1) + (1 x 16^0)

Using the sum formula for a geometric series: 
S = a(1 - r^n) / (1 - r)

where S is the sum of the geometric series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 1, r = 16, and n = 45.

Using the sum formula: 
S = 1(1 - 16^45) / (1 - 16) = 1(1 - 7.378697e+34) / -15

= -4.9180278e+33

Rounding to the nearest integer, we get: 
-4.9180278e+33 ≈ -4928027800000000058445012725024256

The closest answer choice is C, 228.

Find the Numerical Value of by Using the Sum