Question

the sum to infinity of series 54,18,6,2,....Is




The sum to infinity of series 54, 18, 6,2...
is

Answer 1

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Answer 2

Answer:

Sum of series 54,18,6,2 is 81.

Step-by-step explanation:

GIVEN:

            We have a series 54, 18, 6, 2 .....

We can observe that,

This is a geometric progression series.

$a + ar + ar^2 + ar^3 ......$

where $a = 54 \\r = \frac{1}{3}$

Calculation:

Sum of infinite Geometric progression series is..

$S = \frac{a}{1-r}$

Substituting value of a and r

$S = \frac{54}{1-\frac{1}{3} }\\ S = \frac{54}{\frac{3-1}{3} }\\ S = \frac{54}{\frac{2}{3} }\\ S = \frac{27*3}{1}\\ S = 81$

Hence sum of given infinite series is 81.