Question

Find the sum of the series 2, 4, 8, 16…. 256.

Answer 1

Answer:

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Answer 2

Answer:

Find the sum of the series 2, 4, 8, 16…. 256

Answer: the sum of the given series is 510

Step-by-step explanation:

The given question is based on the geometric series

Geometric Series:- geometric series, in mathematics, an infinite series of the form

a + ar + $ar^{2}$ +$ar^{3}$+⋯ $ar^{n-1}$,

where r is known as the common ratio

to calculate the sum of the term the formulae used is given below

$\frac{a(r^{n}-1) }{r^{n}-1 }$

where a is the initial term

r is the common ratio,

n is the number of terms

comparing the term of formula to the question values are

a= 2

r= 2

n= 8 ( the total number of terms are 8)

$\frac{2(2^{8}-1 )}{2-1}$ = $\frac{2(256-1)}{2-1}$

= $2(255)$

= 510

Since ,  the sum of the series is 510

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