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Siruri - exercitiu rezolvat 6

Avem sirul:    

tg 45o, tg 22o 30’,  tg 11o 55’, ….. an

Sa se afle termenul general an = ?

Π / 4 = 180 / 4 = 45o
Π / 8 = 180 / 8 = 22o 30’

adica facem impartirea:

180 o          : 8
16                22o 30’
  20
  16
    4 o = 240’ (arcminute)
            24
              = 0

Π / 12 = 180 / 12 = 11o 55’

Π / 4,  Π / 4 / 2,  Π / 4 / 2 / 2 … an

adica:

Π / 4,  Π / 8,  Π / 16, Π / 32, Π / 64  … an

Se mai poate scrie si altfel:

Π / 4*1,  Π / 4*2,  Π / 4*4, Π / 4*8, Π / 4*16  … an

dar stim ca:

sirul 1, 2, 4, 8, 16……….an 

are termenul general an = 2n-1

1, 2, 4, 8, 16……….2n-1

astfel inlocuind =>

Π / 4 = Π / 4*1 = Π / 4*2n-1

=>

Π / 4*1,  Π / 4*2,  Π / 4*4, Π / 4*8, Π / 4*16,  …… Π / 4*2n-1

deci rezulta in final ca sirul:

tg 45o, tg 22o 30’,  tg 11o 55’, ….. an

are termenul general: