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KVPY2014MathematicsSequences and Series

The value of _ n=0 ¹⁹⁴⁷ 1 2^ n + 2¹⁹⁴⁷ is equal to

Options

  1. A847 2¹⁹⁴⁵
  2. B1946 2¹⁹⁴⁷
  3. C1947 2¹⁹⁴⁷
  4. D1948 2¹⁹⁴⁷

Correct answer

A. 847 2¹⁹⁴⁵

Step-by-step solution

1 1+ 2¹⁹⁴⁷ + 1 2¹⁹⁴⁷+2^ 1947 2 = 1 2^ 1947 2 Similarly & _ n=0 ¹⁹⁴⁷ 1 2⁴+ 2¹⁹⁴⁷ = 974 2¹⁹⁴⁷ = 487 2¹⁹⁴⁵

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