perplexus.info :: Just Math : Rooted to the Floor II

Rooted to the Floor II (Posted on 2014-09-08)

Define F(x) = floor(⁴√x).

Find the value of :

1/F(1) + 1/F(2) +....+ 1/F(2014)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: Pencil and paper solution

Comment 3 of 3 |

(In reply to Pencil and paper solution by Steve Herman)

A reformulation I like:

(16-1)/1 + (81-16)/2 + (256-81)/3 + (625-256)/4 + (1296 - 625)/5 + (2015 - 1296)/6 =

2015/6 + 1296/(5*6) + 625/(4*5) + 256/(3*4) + 81/(2*3) + 16/(2*1) - 1/1 =

(2015*10 + 1296*2 + 625*3 + 256*5 + 81*10 + 16*30 - 60)/60

Posted by Steve Herman on 2014-09-09 10:31:53

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