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[x] + [x+1/n] +[x+ 2/n] +........[x+ (n-1)/n]=[nx] is true
a)for any real no x
b)for any integer x
c){x} is multiple of 1/n
d)for no n.

5 Answers

[x] + [x+1/n] +[x+ 2/n] +........[x+ (n-1)/n]=[nx] is true for all real x.

This is infact Hermite's identity.

PS. and btw next time please try a more meaningful title ?

proof??n sorry bt i cudnt think of any title...

yeah i also think so.For integer i cud prove it but i dnt know how it comes if x is not an integer

http://targetiit.com/iit-jee-forum/posts/10-09-09-greatest-integer-function-11066.html

see this

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω