Question

Ayuda por favor si no saben no respondan doy coronita

Answer 1

Verified answer

Respuesta:

Explicación paso a paso:

[tex]1+2+3+4+...+21[/tex]

[tex]Suma:[/tex]

[tex]1+2+3+...+n[/tex]

[tex]S = \frac{n(n+1)}{2}[/tex]

[tex]n = 21[/tex]

[tex]S = \frac{21(21+1)}{2} = \frac{21(22)}{2} = \frac{462}{2}[/tex]

[tex]S = 231[/tex]

RESPUESTA:

   [tex]231[/tex]

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[tex]10+14+18+22+...=1144[/tex]

PROGRESIÓN ARITMÉTICA:

[tex]a_{1} = 10; a_{2} = 14[/tex]

[tex]Diferencia: d = a_{2} -a_{1}= 14-10 = 4[/tex]

[tex]Suma: S = 1144[/tex]

Último término:

Fórmula:

[tex]a_{x} = a_{1} +(x-1 ) *d[/tex]

[tex]a_{x} =10+ (x-1 ) * 4[/tex]

Fórmula:

[tex]S = \frac{x}{2} (a_{1} +a_{x} )[/tex]

[tex]1144= \frac{x}{2} [ 10+10+(x-1)*4 ][/tex]

[tex]1144 = \frac{x}{2} [ 20+4x-4][/tex]

[tex]2(1144)=x [16+4x], entonces : 2288 = 16x+4x^{2}[/tex]

[tex]4x^{2} +16x -2288=0[/tex]

Factorizando:

[tex]2 [ 2x^{2} +8x-1144] =0[/tex]

[tex](2x)^{2} +8(2x) - 2288= \frac{0}{2}[/tex]

[tex](2x+52)(2x-44) =0[/tex]

[tex]2x +52 = 0 ; 2x -44 = 0[/tex]

[tex]2x = -52[/tex]

[tex]x = -26[/tex]

[tex]2x = 44[/tex]

[tex]x = 22[/tex]

RESPUESTA:

    [tex]x = 22[/tex]

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PROGRESIÓN GEOMÉTRICAS INFINITAS:

[tex]S = 33 + 16.5 + 8.25 + ....[/tex]

[tex]Suma -infinita:[/tex]

[tex]Razon : r = \frac{a_{2} }{a_{1} }= \frac{33}{16.5} = 0.5[/tex]

[tex]S_{\alpha } =\frac{a_{1} }{1-r} = \frac{33}{1-0.5} =\frac{33}{0.5}[/tex]

[tex]S_{\alpha } = 66[/tex]

RESPUESTA:

        [tex]66[/tex]

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PROGRESIÓN ARITMÉTICA:

[tex]S= \sqrt{36} + \sqrt{144} +\sqrt{324} +...+\sqrt{8100}[/tex]

[tex]S = 6+ 12+ 18+... + 90[/tex]

[tex]a _{1} = 6 ; a_{2} = 12[/tex]

[tex]a_{n} = 90[/tex]

[tex]Diferencia: d = 12 -6 = 6[/tex]

[tex]Suma: S = ?[/tex]

[tex]a_{n} = a_{1} + ( n-1 ) *d = 6 + (n-1 ) *6[/tex]

[tex]90 = 6 + 6n -6[/tex]

[tex]90= 6n[/tex]

[tex]n = \frac{90}{6} = 15[/tex]

[tex]S=\frac{n}{2} ( a_{1} +a_{n} )[/tex]

[tex]S = \frac{15}{2} ( 6 +90)[/tex]

[tex]S = (7.5 ) ( 96 ) = 720[/tex]

RESPUESTA:

    [tex]S = 720[/tex]

Answer 2

Respuesta:

Explicación paso a paso:

1+2+3+4+...+211+2+3+4+...+21

Suma:Suma:

1+2+3+...+n1+2+3+...+n

S = \frac{n(n+1)}{2}S=2n(n+1)

n = 21n=21

S = \frac{21(21+1)}{2} = \frac{21(22)}{2} = \frac{462}{2}S=221(21+1)=221(22)=2462

S = 231S=231

RESPUESTA:

   231231

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10+14+18+22+...=114410+14+18+22+...=1144

PROGRESIÓN ARITMÉTICA:

a_{1} = 10; a_{2} = 14a1=10;a2=14

Diferencia: d = a_{2} -a_{1}= 14-10 = 4Diferencia:d=a2−a1=14−10=4

Suma: S = 1144Suma:S=1144

Último término:

Fórmula:

a_{x} = a_{1} +(x-1 ) *dax=a1+(x−1)∗d

a_{x} =10+ (x-1 ) * 4ax=10+(x−1)∗4

Fórmula:

S = \frac{x}{2} (a_{1} +a_{x} )S=2x(a1+ax)

1144= \frac{x}{2} [ 10+10+(x-1)*4 ]1144=2x[10+10+(x−1)∗4]

1144 = \frac{x}{2} [ 20+4x-4]1144=2x[20+4x−4]

2(1144)=x [16+4x], entonces : 2288 = 16x+4x^{2}2(1144)=x[16+4x],entonces:2288=16x+4x2

4x^{2} +16x -2288=04x2+16x−2288=0

Factorizando:

2 [ 2x^{2} +8x-1144] =02[2x2+8x−1144]=0

(2x)^{2} +8(2x) - 2288= \frac{0}{2}(2x)2+8(2x)−2288=20

(2x+52)(2x-44) =0(2x+52)(2x−44)=0

2x +52 = 0 ; 2x -44 = 02x+52=0;2x−44=0

2x = -522x=−52

x = -26x=−26

2x = 442x=44

x = 22x=22

RESPUESTA:

    x = 22x=22

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PROGRESIÓN GEOMÉTRICAS INFINITAS:

S = 33 + 16.5 + 8.25 + ....S=33+16.5+8.25+....

Suma -infinita:Suma−infinita:

Razon : r = \frac{a_{2} }{a_{1} }= \frac{33}{16.5} = 0.5Razon:r=