Are you smarter than Manav D.S.R

Algebra Level 3

If f ( 1 ) = 1 f(1) = 1 , where f ( n ) = n + f ( n 1 ) f(n) = n+ f(n-1) , find f ( 2020 ) f(2020) .


The answer is 2041210.

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1 solution

Swapnil Das
Mar 22, 2016

As f ( n ) = n + f ( n 1 ) f(n)=n+f(n-1) ,

f ( 2020 ) = 2020 + [ 2019 + 2018 + 2017 + . . . + f ( 1 ) ] f(2020)=2020+[2019+2018+2017+...+f(1)] = n = 1 2020 n = 2041210 \sum _{ n=1 }^{ 2020 }{ n }=2041210 .

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