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Buktikan masing-masing ketidaksamaan eksponen di bawah ini. c.

Pertanyaan

Buktikan masing-masing ketidaksamaan eksponen di bawah ini.

c. 5 to the power of straight n plus 5 less than 5 to the power of straight n plus 1 end exponent 

Pembahasan Soal:

Pembuktian dengan menggunakan induksi matematika dimana

untuk n =1 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of 1 plus 5 end cell less than cell 5 to the power of 1 plus 1 end exponent end cell row 10 less than cell 25 rightwards arrow terbukti space end cell end table

untuk n = k akan diasumsikan terbukti

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of straight k plus 5 end cell less than cell 5 to the power of straight k plus 1 end exponent rightwards arrow terbukti end cell end table

akan dibuktikan untuk n = k+1 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of straight k plus 1 end exponent plus 5 end cell less than cell 5 to the power of left parenthesis straight k plus 1 right parenthesis plus 1 end exponent end cell row cell 5 to the power of straight k plus 5 to the power of 1 plus 5 end cell less than cell 5 to the power of left parenthesis straight k plus 1 right parenthesis plus 1 end exponent end cell row cell 5 to the power of straight k plus 5 plus 5 to the power of 1 end cell less than cell 5 to the power of left parenthesis straight k plus 1 right parenthesis plus 1 end exponent end cell row cell 5 to the power of straight k plus 1 end exponent plus 5 end cell less than cell 5 to the power of left parenthesis straight k plus 1 right parenthesis plus 1 end exponent rightwards arrow terbukti end cell end table

jadi terbukti untuk 5 to the power of straight n plus 5 less than 5 to the power of straight n plus 1 end exponent karena table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of straight k plus 1 end exponent plus 5 end cell less than cell 5 to the power of left parenthesis straight k plus 1 right parenthesis plus 1 end exponent end cell end table

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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