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in Mathematics by (67.9k points)

The sum to 2n terms of the series 3/4 + 7/4 + 15/16 + 31/16 + 63 + 64 + 127/64 + ..... is

(a) 3n - 2/3(1 - 1/4n)

(b)  3n - 10/21(1 - 1/4n)

(c) 3n - 13/21 1/4n

(d) None of these

1 Answer

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Best answer

Correct option   (a) 3n - 2/3(1 - 1/4n)

Explanation:

Given expression

= (1 - 1/4) + (2 - 1/4) + (1 - 1/16) + (2 - 1/16) +  .........2n terms

= 3n –2(1/4 + 1/16 + ...n terms)

= 3n - 2/3(1 - 1/4n)

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