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Question
Evaluate:
`("a"^(2"n"+1)xx"a"^((2"n"+1)(2"n"-1)))/("a"^("n"(4"n"-1))xx("a"^2)^(2"n"+3)`
Sum
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Solution
`("a"^(2"n"+1)xx"a"^((2"n"+1)(2"n"-1)))/("a"^("n"(4"n"-1))xx("a"^2)^(2"n"+3)`
`=("a"^(2"n"+1)xx"a"^(4"n"^2-1))/("a"^(4"n"^2-"n")xx"a"^(4"n+6"`
`="a"^(4"n"+2"n")/("a"^(4"n"^2+3"n"+6)`
`="a"^(4"n"^2+2n-(4n^2+3n+6)`
`="a"^(4"n"^2+2n-4n^2-3n-6)`
`="a"^(-"n"-6)`
`="a"^-("n"+6)`
`=1/("a"^("n"+6)`
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