The sum of the first 20 terms of the series 1 + 3 2 + 7 4 + 15 8 + 31 16 + … is

The sum of the first 20 terms of the series 1+32+74+158+3116+… is
  1. 39+1219
  2. 38+1220
  3. 38+1219
  4. 39+1220

Solution

1+32+74+158+3116+…

=2-1+2-12+2-14+2-18+2-116+…upto 20 terms

=40-1+12+14+18+…upto 20 terms

=40-1-12201-12=40-2+1219=38+1219

Asked in: JEE Main 2018 (16 Apr Online)

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