Math - Geometric Series

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Find the sum of the geometric series 128 - 64 + 32 - . . . to 8 terms.

a) 85
b) 225
c) 86
d) 85/2
e) not possible

  • Math - Geometric Series -

    r = -64/128 = -1/2
    a = 128

    sum(8) = 128( 1 - (1/2)^8 / (1+1/2)
    = 128(255/256)(2/3) = 85

  • Math - Geometric Series -

    With only 8 terms, it's easier for me to do the addition than remember the formula.

    Adding in pairs, successive pairs are lower by a factor of 4.
    64 + 16 + 4 + 1 = 85

  • Math - Geometric Series -

    128-64+32-16+8-4+2-1=64+16+4+1=80+5=85(!)

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