Question

Find the sum of the series 32, 16, 8, 4, upto infinity.

Answer 1

Step-by-step explanation:

s infite =a/(1-r)

32 /(1-1/2)

32/((1/2)

64

Answer 2

The sum of infinite terms of given series is 64

Step-by-step explanation:

Given : series  32 , 16 ,  8,  4 ,............

To find : The sum of infinite terms

Now as we can see

$\dfrac{II}{I} =\dfrac{16}{32}=\dfrac{1}{2} \\\\\\\dfrac{III}{II} =\dfrac{8}{16}=\dfrac{1}{2}$

Therefore the ratio is same the series forms a G.P.

Now the sum of infinite terms of G.P. is given by

$S_ \infty = \dfrac{a}{1-r}$   where a is first term and r is common ratio and  0<r<1

Now

according to question

a= 32 , $r= \dfrac{1}{2}$

So we have

$S_\infty= \dfrac{32}{1-\dfrac{1}{2} } = \dfrac{32}{\dfrac{2-1}{2} } = 32\times 2= 64$

Hence, the sum of infinite terms of given series is 64

#Learn more

Find the sum of 10 terms of gp, first term and common ratio are 8 and 3

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