Jawaban:

Nilai dari \left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= 7\frac{1}{20}

20

1

. Simak pembahasan mengenai notasi sigma berikut.

Pembahasan

Rumus umum notasi sigma adalah

\left \sum {{n} \atop {i=1}} \right. f(x_{i})f(x

i

) = f(x_{1})f(x

1

) + f(x_{2})f(x

2

) + f(x_{3})f(x

3

) + .... + f(x_{n})f(x

n

)

Maka nilai dari \left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

adalah

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= \frac{(-2)^{2}}{(-2) + 3}

(−2)+3

(−2)

2

+ \frac{(-1)^{2}}{(-1) + 3}

(−1)+3

(−1)

2

+ \frac{0^{2}}{0 + 3}

0+3

0

2

+ \frac{1^{2}}{1 + 3}

1+3

1

2

+ \frac{2^{2}}{2 + 3}

2+3

2

2

+ \frac{3^{2}}{3 + 3}

3+3

3

2

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= \frac{4}{1}

1

4

+ \frac{1}{2}

2

1

+ \frac{0}{3}

3

0

+ \frac{1}{4}

4

1

+ \frac{4}{5}

5

4

+ \frac{9}{6}

6

9

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= 4 + \frac{1}{2}

2

1

+ 0 + \frac{1}{4}

4

1

+ \frac{4}{5}

5

4

+ \frac{3}{2}

2

3

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= 4 + \frac{1}{2}

2

1

+ \frac{1}{4}

4

1

+ \frac{4}{5}

5

4

+ \frac{3}{2}

2

3

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= \frac{80}{20}

20

80

+ \frac{10}{20}

20

10

+ \frac{5}{20}

20

5

+ \frac{16}{20}

20

16

+ \frac{30}{20}

20

30

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= \frac{80 + 10 + 5 + 16 + 30}{20}

20

80+10+5+16+30

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= \frac{141}{20}

20

141

\left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

= 7\frac{1}{20}

20

1

Jadi nilai dari \left \sum {{3} \atop {k=-2}} \right. \frac{k^{2}}{k + 3}

k+3

k

2

adalah 7\frac{1}{20}

20

1

Pelajari lebih lanjut

Menyatakan deret geometri dalam bentuk notasi sigma yomemimo.com/tugas/23213682

Menentukan banyak pola pada suku ke- n deret geometri yomemimo.com/tugas/23191664

---------------------------------------------------

Detil jawaban

Kelas: 11

Mapel: Matematika

Bab: Notasi sigma

Kode: 11.2.

Kata kunci: notasi sigma, jumlah, nilai