Use the formula for the sum of a geometric series to find the sum. (Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 100/81 + 10/9 + 1 + 9/10 + 81/100 + ⋯ =

The sum of this geometric series to infinity = (1000/81) = 12.35

Step-by-step explanation:

The sum to infinity of a geometric series is given as

S = a/(1 - r)

where a = first term = (100/81)

r = common ratio = [(n + 1)th term] ÷ [nth term] = (second term) ÷ (first term)

r = (10/9) ÷ (100/81) = (9/10) = 0.9

S = a ÷ (1 - r)

S = (100/81) ÷ (1 - 0.9)

S = (100/81) ÷ 0.1

S = (1000/81) = 12.35

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