If the set R = {( a , b ) : a + 5 b = 42 , a , b ∈ N } has m elements and ∑ n = 1 m ( 1 − i n ! ) = x + i y , where i = − 1 , then the value of m + x + y is

Question

If the set R = {( a , b ) : a + 5 b = 42 , a , b ∈ N } has m elements and ∑ n = 1 m ​ ( 1 − i n ! ) = x + i y , where i = − 1 ​ , then the value of m + x + y is

TestHub · Accepted Answer

​ a + 5 b = 42 , a , b ∈ N a = 42 − 5 b , b = 1 , a = 37 b = 2 , a = 32 b = 3 , a = 27 ⋮ b = 8 , a = 2 ​ R has " 8 " elements ⇒ m = 8 ​ n = 1 ∑ 8 ​ ( 1 − i n ! ) = x + i y for n ≥ 4 , i n ! = 1 ⇒ ( 1 − i ) + ( 1 − i 2 ! ) + ( 1 − i 3 ! ) = 1 − I + 2 + 1 + 1 = 5 − I = x + i y m + x + y = 8 + 5 − 1 = 12 ​

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