Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Given n4 n for a fixed positive integer n ≥ 2, prove that (n + 1)4 n + 1.
Sol. Given that n4 < 10n for n for a fixed + ve integer n ≥2. To prove that (n + 1)4 , 10n + 1 Proof : Since n4 < 10n ⇒ 10n4 < 10n + 1 . . . . . . . . . . . . . . . . . . (1) So it is sufficient to prove that (n + 1)4 < 10n4 Now (n + 1/n)4 = (1 + 1/n)4 ≤ (1 + 1/2)4 [∵ n ≥ 2] = 81/16 < 10 ⇒ (n + 1)4 < 10n4 . . . . . . . . . . . . . . . . . . . . . . . .(2) From (1) and (2), (n + 1)4 < 10n + 1
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -