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Pertanyaan

Dengan menuliskan jumlah lengkap diruas kiri dan kanan, buktikanlah:

sum from i equals 3 to 7 of i squared equals sum from i equals 1 to 5 of open parentheses i plus 2 close parentheses squared 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

terbukti bahwa sum from i equals 3 to 7 of i squared equals sum from i equals 1 to 5 of open parentheses i plus 2 close parentheses squared.

Pembahasan

Ingat kembali sifat mutlak:

sum from k equals s to s of a subscript k equals a subscript s semicolon space s equals 1 comma space 2 comma space 3 comma space horizontal ellipsis comma space n open parentheses bilangan space asli close parentheses 

-Menentukan nilai ruas kiri sum from i equals 3 to 7 of i squared 

table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 3 to 7 of i squared end cell equals cell 3 squared plus 4 squared plus 5 squared plus 6 squared plus 7 squared end cell row blank equals cell 9 plus 16 plus 25 plus 36 plus 49 end cell row blank equals 135 end table 

-Menentukan nilai ruas kanan sum from i equals 1 to 5 of open parentheses i plus 2 close parentheses squared 

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 1 to 5 of open parentheses i plus 2 close parentheses squared end cell equals cell open parentheses 1 plus 2 close parentheses squared plus open parentheses 2 plus 2 close parentheses squared plus open parentheses 3 plus 2 close parentheses squared plus open parentheses 4 plus 2 close parentheses squared plus open parentheses 5 plus 2 close parentheses squared end cell row blank equals cell open parentheses 3 close parentheses squared plus open parentheses 4 close parentheses squared plus open parentheses 5 close parentheses squared plus open parentheses 6 close parentheses squared plus open parentheses 7 close parentheses squared end cell row blank equals cell 9 plus 16 plus 25 plus 36 plus 49 end cell row blank equals 135 end table end style 

Sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 3 to 7 of i squared end cell equals cell sum from i equals 1 to 5 of open parentheses i plus 2 close parentheses squared end cell row 135 equals 135 end table 

Dengan demikian terbukti bahwa sum from i equals 3 to 7 of i squared equals sum from i equals 1 to 5 of open parentheses i plus 2 close parentheses squared.

23

1.0 (1 rating)

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