Calcolare la somma della serie:
\sum ((-1)^n)*((2n +1)/n!)
n>=0
∑ (–1)ⁿ(2n + 1)/n! =
n≥0
∑ (–1)ⁿ(2n/n! + 1/n!) =
2 ∑ (–1)ⁿn/n! + ∑ (–1)ⁿ/n! =
. n≥1 . . . . . . . n≥0
2 ∑ (–1)ⁿ/(n–1)! + ∑ (–1)ⁿ/n! =
. n≥1 . . . . . . . . . n≥0
–2 ∑ (–1)ⁿ/n! + ∑ (–1)ⁿ/n! =
. n≥0 . . . . . . . n≥0
– ∑ (–1)ⁿ/n! =
. n≥0
–e‾¹
ciao
Comments
∑ (–1)ⁿ(2n + 1)/n! =
n≥0
∑ (–1)ⁿ(2n/n! + 1/n!) =
n≥0
2 ∑ (–1)ⁿn/n! + ∑ (–1)ⁿ/n! =
. n≥1 . . . . . . . n≥0
2 ∑ (–1)ⁿ/(n–1)! + ∑ (–1)ⁿ/n! =
. n≥1 . . . . . . . . . n≥0
–2 ∑ (–1)ⁿ/n! + ∑ (–1)ⁿ/n! =
. n≥0 . . . . . . . n≥0
– ∑ (–1)ⁿ/n! =
. n≥0
–e‾¹
ciao