Let ∑ k = 1 ∞ u k be an infinite series, and let be the sequence of partial sums for the series: If lim n → ∞ s n = S , where is a real number, then the infinite series converges and ∑ k = 1 ∞ u k = S . If lim n → ∞ s n does not have a finite limit, then the infinite series diverges.
The formula for the sum of an infinite series is a/(1-r), where a is the first term in the series and r is the common ratio i.e. the number that each term is multiplied by to get the next term in the sequence.
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Step-by-step explanation:
Let ∑ k = 1 ∞ u k be an infinite series, and let be the sequence of partial sums for the series: If lim n → ∞ s n = S , where is a real number, then the infinite series converges and ∑ k = 1 ∞ u k = S . If lim n → ∞ s n does not have a finite limit, then the infinite series diverges.
Answer:
The formula for the sum of an infinite series is a/(1-r), where a is the first term in the series and r is the common ratio i.e. the number that each term is multiplied by to get the next term in the sequence.