Calcolatrice di serie e somme con passi

Questa calcolatrice cercherà di trovare la somma infinita di serie aritmetiche, geometriche, di potenze e binomiali, nonché la somma parziale, con i passi indicati (se possibile). Verrà inoltre verificato se la serie converge.

Sum of:

Variable:

Start Value:

If you need

$\displaystyle{\large{-\infty}}$ , type -inf.

End Value:

If you need

$\displaystyle{\large{\infty}}$ , type inf.

If you need a binomial coefficient

$\displaystyle{\large{{C}{\left({n},{k}\right)}={\left(\begin{array}{c}{n}\\{k}\\ \end{array}\right)}}}$ , type binomial(n,k).

If you need a factorial

$\displaystyle{\large{{n}!}}$ , type factorial(n).

Variables in the bounds are assumed to be positive.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Answer

Your input: calculate $\sum_{n=1}^{\infty} 3^{- n}$

$\sum_{n=1}^{\infty} 3^{- n}$ is an infinite geometric series with the first term $b=\frac{1}{3}$ and the common ratio $q=\frac{1}{3}$ .

By the ratio test, it is convergent.

Its sum is $S=\frac{b}{1-q}=\frac{1}{2}$ .

Therefore,

${\color{red}{\left(\sum_{n=1}^{\infty} 3^{- n}\right)}}={\color{red}{\left(\frac{1}{2}\right)}}$

Hence,

$\sum_{n=1}^{\infty} 3^{- n}=\frac{1}{2}$

Answer: $\sum_{n=1}^{\infty} 3^{- n}=\frac{1}{2}=0.5$

Calcolatrice di serie e somme con passi

Calcolo di serie e somme passo dopo passo

Answer