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Question

Let S=9999n=11(n+n+1)(4n+4n+1), then S is equal to

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Solution

S=9999n=11(n+n+1)(4n+4n+1)

S=9999n=11×(4n44n+1)(n+n+1)(4n+4n+1)×(4n4n+1)

S=9999n=1(4n4n+1)(n+n+1)(nn+1)

S=9999n=14n+14n

S=4241+4342+...+41000049999
S=101=9

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