Translation for "osasummasta" to english

Osasummasta

• partial sum
• part of the amount

Translation examples

partial sum

Olkoon {an} sarja ja olkoon s k = a 1 + ⋯ + a k {\displaystyle s_{k}=a_{1}+\cdots +a_{k}} , sarjan ∑ n = 1 ∞ a n . {\displaystyle \sum _{n=1}^{\infty }a_{n}.} k:s osasumma.
Let ( a n ) n = 1 ∞ {\displaystyle (a_{n})_{n=1}^{\infty }} be a sequence, and let s k = a 1 + ⋯ + a k = ∑ n = 1 k a n {\displaystyle s_{k}=a_{1}+\cdots +a_{k}=\sum _{n=1}^{k}a_{n}} be its kth partial sum.

Sarjaa {an} kutsutaan Cesàro-summautuvaksi, jos Cesàron summa A ∈ R {\displaystyle A\in \mathbb {R} } , jos sen keskiarvo osasummista s k {\displaystyle s_{k}} lähenee A {\displaystyle A} :ta: lim n → ∞ 1 n ∑ k = 1 n s k = A . {\displaystyle \lim _{n\to \infty }{\frac {1}{n}}\sum _{k=1}^{n}s_{k}=A.} Toisin sanoen siis äärettömän sarjan Cesàro-summa on sarjan ensimmäisten osasummien 1, ..., n aritmeettisen keskiarvon raja-arvo, kun n lähestyy ääretöntä.
The sequence (an) is called Cesàro summable, with Cesàro sum A ∈ ℝ, if, as n tends to infinity, the arithmetic mean of its first n partial sums s1, s2, ..., sn tends to A: lim n → ∞ 1 n ∑ k = 1 n s k = A . {\displaystyle \lim _{n\to \infty }{\frac {1}{n}}\sum _{k=1}^{n}s_{k}=A.} The value of the resulting limit is called the Cesàro sum of the series ∑ n = 1 ∞ a n . {\displaystyle \textstyle \sum _{n=1}^{\infty }a_{n}.} If this series is (conditionally) convergent, then it is Cesàro summable and its Cesàro sum is the usual sum.