Happy New Year!

Algebra Level 4

∑ i = 0 2016 ( 2016 i ) = 1 a ! + ∑ i = 0 b i ( i + 1 ) ! + ∑ i = 0 c 2 i \large \sum_{i=0}^{2016} \dbinom{2016}i = \dfrac1{a!} + \sum_{i=0}^b \dfrac i{(i+1)!} + \sum_{i=0}^c 2^i

If a , b a,b and c c are positive integers satisfying the equation above, find a − b + c a-b+c .


The answer is 2016.

Budi Utomo by Budi Utomo , 23, Indonesia

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1 solution

Budi Utomo
Jan 8, 2016

4 Helpful 0 Interesting 1 Brilliant 0 Confused

Happy New Year :) The problem is beautiful.

Pulkit Gupta - 5 years, 5 months ago

Great, Budi.

It is interesting to note that 2016 = 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + 2^10.

Jeganathan Sriskandarajah - 5 years, 4 months ago

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