Multiple choice

Find the sum of the series given below: 2 + 1 + 4 + 2 + 8 + 3 + 16 + 4 + 32 + 5 + … + 20th term

  1. 2092

  2. 2045

  3. 1987

  4. 2101

  5. 2100
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D Correct answer
Explanation

The series is (2+1) + (4+2) + (8+3) + (16+4) + ... = 3 + 6 + 11 + 20 + ... This is not a standard arithmetic or geometric series. Breaking it into two series: (2+4+8+... 10 terms) + (1+2+3+... 10 terms). Sum = 2*(2^10 - 1)/(2-1) + 10/2 * (1+10) = 2 * 1023 + 5 * 11 = 2046 + 55 = 2101.

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