How do you find the sum of the infinite geometric series a1=26 and r=1/2?

Answer 1

#52#

Sum of infinite geometric series is given by #S=a_1/(1-r)# Where #S# is the sum of the series #a_1# is the first term and #r# is the common ration. #implies S=26/(1-1/2)=52/(2-1)=52/1=52# #implies S=52# Hence the sum of the given infinite geometric series is #52#.

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Answer 2

Serenity Johnson

To find the sum of the infinite geometric series with first term ( a_1 = 26 ) and common ratio ( r = \frac{1}{2} ):

Use the formula for the sum of an infinite geometric series: ( S = \frac{a_1}{1 - r} ).
Substitute the given values: ( S = \frac{26}{1 - \frac{1}{2}} ).
Simplify: ( S = \frac{26}{1 - \frac{1}{2}} = \frac{26}{\frac{1}{2}} = 26 \times 2 = 52 ).

Therefore, the sum of the infinite geometric series is 52.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.