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Tentukan himpunan bilangan asli untuk n agar pernyataan berikut menjadi benar. 3n≥2n+1

Pertanyaan

Tentukan himpunan bilangan asli untuk n agar pernyataan berikut menjadi benar.

3 to the power of straight n greater or equal than 2 to the power of straight n plus 1 end exponent 

A. Acfreelance

Master Teacher

Mahasiswa/Alumni UIN Walisongo Semarang

Jawaban terverifikasi

Jawaban

himpunan bilangan asli dari 3 to the power of straight n greater or equal than 2 to the power of straight n plus 1 end exponent adalah straight x greater than 1

Pembahasan

Mencari himpunan dengan mensubsitusikan bilangan asli

Untuk n =1 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of straight n end cell greater or equal than cell 2 to the power of straight n plus 1 end exponent end cell row cell 3 to the power of 1 end cell greater or equal than cell 2 to the power of 1 plus 1 end exponent end cell row 3 greater or equal than cell 4 rightwards arrow Bukan space merupakan space himpunan space end cell end table

Untuk n =2 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of straight n end cell greater or equal than cell 2 to the power of straight n plus 1 end exponent end cell row cell 3 squared end cell greater or equal than cell 2 to the power of 2 plus 1 end exponent end cell row 9 greater or equal than cell 5 rightwards arrow merupakan space himpunan space end cell end table

Untuk n =3 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of straight n end cell greater or equal than cell 2 to the power of straight n plus 1 end exponent end cell row cell 3 cubed end cell greater or equal than cell 2 to the power of 3 plus 1 end exponent end cell row 27 greater or equal than cell 16 rightwards arrow merupakan space himpunan space end cell end table

Untuk n = 4 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of straight n end cell greater or equal than cell 2 to the power of straight n plus 1 end exponent end cell row cell 3 to the power of 4 end cell greater or equal than cell 2 to the power of 4 plus 1 end exponent end cell row 81 greater or equal than cell 32 rightwards arrow merupakan space himpunan space end cell end table

Untuk n = 5 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of straight n end cell greater or equal than cell 2 to the power of straight n plus 1 end exponent end cell row cell 3 to the power of 5 end cell greater or equal than cell 2 to the power of 5 plus 1 end exponent end cell row 243 greater or equal than cell 64 rightwards arrow merupakan space himpunan space end cell end table

Jadi himpunan bilangan asli dari 3 to the power of straight n greater or equal than 2 to the power of straight n plus 1 end exponent adalah straight x greater than 1

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