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.)

Pencil and paper solution

| Comment 2 of 3 |

1^4 = 1

2^4 = 16

3^4 = 81

4^4 = 256

5^4 = 625

6^4 = 1296

7^4 = 2401

So there are 15 terms equal to 1/1, (81-16) terms equal to 1/2, etc.

Final answer =

(16-1)/1 + (81-16)/2 + (256-81)/3 + (625-256)/4 + (1296 - 625)/5 + (2015 - 1296)/6 = 27127/60, which is approx 452.11667

Posted by Steve Herman on 2014-09-08 22:00:55

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