can anyone prove it..SIMPLE..

JEE Mains 2015 Guidance › Algebra questions › can anyone prove it..SIMPLE..

Given that n⁴<10ⁿ for a fixed positive integer nâ‰¥2, then prove that (n+1)⁴<10ⁿ⁺¹

#Mathematics #Algebra

UP 0 DOWN 0 0 7
Post on FacebookPost anonymously?

7 Answers

62

Lokesh Verma ·2009-01-18 22:15:48

hey if this is true for n..

then just substitute n+1 instead of n

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

Honey Arora ·2009-01-18 22:18:10

I think it cn be proved by using PMI

UP 0 DOWN 0
Post on FacebookPost anonymously?

13

MAK ·2009-01-18 22:37:59

can v do lyk dis...!!!

n⁴<10ⁿ
=> log_nn < log₄10
=> log_n+1n+1 < log₄10

=> (n+1)⁴ < 10ⁿ⁺¹

correct me if i'm wrong...

UP 0 DOWN 0
Post on FacebookPost anonymously?

13

Ð”Ð²Ò¥Ñ—ÑuÏ now in medical c ·2009-01-18 22:41:11

nice one.. MAK

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

prateek punj ·2009-01-19 01:55:29

but i agree with nishant bhaiya....
if it is true for n then it also true for n+1....

UP 0 DOWN 0
Post on FacebookPost anonymously?

13

MAK ·2009-01-19 02:01:28

how can v say it directly bhaiya...?

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

prateek punj ·2009-01-19 02:12:14

we do the same in mathematical induction...

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ 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