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The answer would be option D.

The theorems required for this are elegantly explained in the following youtube link

https://www.youtube.com/watch?v=OjvF7OcdNiQ

$∑^{20}_{k=0}$(2k + 1)C(41, 2k + 1)

= 41* $∑^{20}_{k=0}$C(40, 2k) 

Now the sum of Even terms would be equal to odd terms as per theorems in the youtube link hence each of those sums would be $2^{39}$

Hence the answer is 41 * $2^{39}$

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