Calculo Multi

SUMAS PARCIALES

Javier navas

Carlos jaimes

Luis Alberto rivera

Hovan pinto herrera

∑▒〖 5/(n(n+1))〗

S1 = 5/2

S2 =5/2+5/6= 10/3

S3 =5/2+5/6+5/12=15/4

Sn =5n/(n+1)

lim┬(n→∞)⁡〖Sn↔ lim┬(n→∞)⁡〖5n/(n+1)〗 〗= (5n/n)/((n^2+n)/n)= (5n/n)/(n^2/n+1/n)= 5/(n/n)= 5/1= 5

La sucesión converge a 5

∑▒〖1/3-1/(n+3)〗

S1= 1/12

S2= 2/15

S3= 1/6

S4= 4/21

Sn= n/(3n+9)

lim┬(n→∞)⁡〖n/(3n+9)= (n/n)/(3n/n+9/n) = 1/(3+9/n)〗 = 1/(3+0) = 1/3

La sucesión converge a 1/3

GEOMETRICAS

∑▒1/3^n

1/(3*3^(n-1) )= 1/3*1/3^(n-1) → 1/3*(1/3)^(n-1)

1/3<1→CONVERGE

∑▒〖3^2n*2^(1-n) 〗

9^n*2*2^(-1)= 2* 9^n/2^n = 2*(9/2)^n = 2* 9/2*(9/2)^(n-1)

9/2>1 →DIVERGE

INTEGRALES

∑▒〖〖3n〗^2 n^3 〗

∫▒〖〖3n〗^2 n^(3 ) dn =〗

u= n^3

du= 〖3n〗^2 dn

∫▒〖u du= u^2/2〗 → (n^3 )^2/2 = n^6/2

∑▒(2n-7 )/(n^2- 7n+10)

∫▒〖(2n-7)/(n^2- 7n-10) dn=〗

u= n^2- 7n-10

du= 2n-7 dn

∫▒u/du=ln⁡u → ln⁡〖n^2- 7n+10

SUMAS PARCIALES

Javier navas

Carlos jaimes

Luis Alberto rivera

Hovan pinto herrera

∑▒〖 5/(n(n+1))〗

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