21 uždavinys

20 uždavinys22 uždavinys

Sprendimas:

$S_{1}$ = $4\cdot 1^{2}+4\cdot 1$ = $4+4$ = $8$

Atsakymas: 8

Sprendimas:

$S_{2n}$ = $4\cdot (2\cdot n)^{2}+4\cdot (2\cdot n)$

$S_{n}$ = $4\cdot n^{2}+4\cdot n$

4* ( 2* n)^²+ 4* ( 2* n) =

11

/ 3

* ( 4* n^²+ 4* n)

4* ( 2* n)^²+ 4* ( 2* n) =

11

/ 3

* ( 4* n^²+ 4* n) $4\cdot (2\cdot n)^{2}+4\cdot (2\cdot n)$ = $\frac{11}{3}\cdot (4\cdot n^{2}+4\cdot n)$

16* n^²+ 4* ( 2* n) =

11

/ 3

* ( 4* n^²+ 4* n) $16\cdot n^{2}+4\cdot (2\cdot n)$ = $\frac{11}{3}\cdot (4\cdot n^{2}+4\cdot n)$

16* n^²+ 8* n =

11

/ 3

* ( 4* n^²+ 4* n) $16\cdot n^{2}+8\cdot n$ = $\frac{11}{3}\cdot (4\cdot n^{2}+4\cdot n)$

16* n^²+ 8* n =

11

/ 3

* 4* n^²+

11

/ 3

* 4* n $16\cdot n^{2}+8\cdot n$ = $\frac{11}{3}\cdot 4\cdot n^{2}+\frac{11}{3}\cdot 4\cdot n$

16* n^²+ 8* n =

44* n^²

/ 3

+

11

/ 3

* 4* n $16\cdot n^{2}+8\cdot n$ = $\frac{44\cdot n^{2}}{3}+\frac{11}{3}\cdot 4\cdot n$

16* n^²+ 8* n =

44* n^²

/ 3

+

44* n

/ 3

$16\cdot n^{2}+8\cdot n$ = $\frac{44\cdot n^{2}}{3}+\frac{44\cdot n}{3}$

16* n^²-

44* n^²

/ 3

+ 8* n =

44* n

/ 3

$16\cdot n^{2}-\frac{44\cdot n^{2}}{3}+8\cdot n$ = $\frac{44\cdot n}{3}$

16* n^²-

44* n^²

/ 3

+ 8* n-

44* n

/ 3

= 0 $16\cdot n^{2}-\frac{44\cdot n^{2}}{3}+8\cdot n-\frac{44\cdot n}{3}$ = 0

4* n^²

/ 3

+ 8* n-

44* n

/ 3

= 0 $\frac{4\cdot n^{2}}{3}+8\cdot n-\frac{44\cdot n}{3}$ = 0

4* n^²

/ 3

-

20* n

/ 3

= 0 $\frac{4\cdot n^{2}}{3}-\frac{20\cdot n}{3}$ = 0

n = 0 $n$ = 0

4* n

/ 3

-

20

/ 3

= 0 $\frac{4\cdot n}{3}-\frac{20}{3}$ = 0

4* n

/ 3

= 0+

20

/ 3

$\frac{4\cdot n}{3}$ = $0+\frac{20}{3}$

4* n

/ 3

=

20

/ 3

$\frac{4\cdot n}{3}$ = $\frac{20}{3}$

4* n =

20* 3

/ 3

$4\cdot n$ = $\frac{20\cdot 3}{3}$

4* n = 20 $4\cdot n$ = $20$

n =

20

/ 4

$n$ = $\frac{20}{4}$

n = 5 $n$ = $5$

Atsakymas: n = 5

20 uždavinys22 uždavinys