Question

how many terms of the series 64+32+16+.... .... must be taken so that the sum may be 255/2 .

Answer 1

Step-by-step explanation:

Common ratio = 1/2

Sn = a + ar + a r ² + -----------ar^( n - 1 )

r Sn = ar + ar ² + ----------------------------ar^n

(1 - r ) Sn = a - a r^n

Sn = a (1 - r^n ) / ( 1 - r ) = 255/2

64 [ 1 - (1/2)^n ] = (255/2) ( 1/2)

1 - (1/2)^n = 255 / [ 4 x 64 ]

1 - 255 / 256 = (1/2)^n

1 / 256 = (1/2)^n

2^n = 256

n = 8 An