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Question

If 4k=0(34k(4k)!)(xkk!)=323, then the largest value of x is

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Solution

4k=0(34k(4k)!)(xkk!)=4k=0(34k(4k)!)(xkk!)4!4!=4k=0(4!34kxk(4k)!k!)14!=4k=04Ck34kxk4!=(3+x)44!
Therefore,
(3+x)44!=323(3+x)4=28(x+3)=±4
x=1 or 7
So, the largest real value of x is 1.

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