Problem 6

Probability Level 4

The sum of the coefficients of all the integrals powers of xx in the expansion of (1+2x)40{ \left( 1+2\sqrt { x } \right) }^{ 40 } If the sum can be represented as 1A(3B+1),\frac { 1 }{ A } \left( { 3 }^{ B }+1 \right), where A,BA, B are positive integers less than 100. Find the value of A+B+1A+B+1

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