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Find the sum of the series: 2*C(20,0) + 5*C(20,1) + 8*C(20,2) + 11*C(20,3) +... + 62*C(20,20).

1. 2²⁴
2. 2²⁵
3. 2²⁶
4. 2²³

Correct answer: 2²⁵

Solution

Sum = sum_(r=0)²⁰ (3r+2)*C(20,r) = 3*sum(r*C(20,r)) + 2*sum(C(20,r)) = 3*20*2¹⁹ + 2*2²⁰ = 60*2¹⁹ + 4*2¹⁹ = 64*2¹⁹ = 2⁶*2¹⁹ = 2²⁵.

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