- #1
Kenshin
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If the nth partial sum of a series Σ Ak is Sn = (n-1)/(n+1) , find Ak . Does Σ Ak converge?
i looked in my math book and can't find how to do this.
i looked in my math book and can't find how to do this.
Kenshin said:Ak= 2/x^2+3x+2. so you subtrack Sn+1-Sn. can u show me how that works. it just seems weird that, that is all u have to do. thanks
Kenshin said:Ak= 2/x^2+3x+2. so you subtrack Sn+1-Sn. can u show me how that works. it just seems weird that, that is all u have to do. thanks
matt grime said:I don't think you mean if and only if in part 2) there.
HallsofIvy said:2) Since Σ A(k) converges if and only if the sequence of partial sums converges,
The formula for the Nth partial sum of a series is Sn = (n-1)/(n+1), where n represents the number of terms in the series.
The Nth partial sum of a series is calculated by multiplying the number of terms (n) by the value of the series at that term, and then adding all of these values together.
The formula (n-1)/(n+1) represents the sum of the first n terms in a series, where n is the number of terms in the series. It is also known as the Nth partial sum of the series.
The Nth partial sum of a series is useful in mathematical analysis as it allows us to approximate the value of an infinite series by considering only a finite number of terms. This can help us understand the behavior and convergence of a series.
No, the Nth partial sum of a series can only provide an approximation of the value of an infinite series. To find the exact value, we would need to consider an infinite number of terms, which is not possible in most cases.