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Question:

The sum of the first 20 terms of the series 1 + 3/2 + 7/4 + 15/8 + 31/16 + ...., is?

39+1220

38+1220

39+1219

38+1219

Solution:

Tn = 2n - n - 1
∑20n=1Tn = ∑20n=1(2n - n -1) = ∑20n=12n - ∑20n=1n - ∑20n=11
= 2(220 - 1)/(2-1) - (20)(21)/2 - 20
= 221 - 2 - 210 - 20
= 2097152 - 230
= 2096922
= 38 + 1219
Hence, the answer is option (D)