Let r E No and n E N. In this problem, a general formula for o,(n) is found. (a) Let n e N. Prove that (ple+1)r – 1 o,(n) = II (2 p* – 1 pe||n

Q: 3. Prove or disprove the given statement. (a) If x e R, and x + 0, then 2x > x. (b) If n e Z*, then…

A: Given: (a) If x∈R, and x≠0,then 2x>x (b) If n∈Z+, then 2n-1>0

Q: 00 Eak, |a| < 1 k=2

A: ∑k=2∞ak,  a&lt;1

Q: S Vī dx (2/3) x3/2 + c O (3/2) x3/2 + c (2/3) x2/3 + c O none of the above

A:

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: S ze dz. |2|=1 Find

A:

Q: 4. Show that inf {1+ ¼n: n EN} = 1 %3D

A: I have proved that the sequence is decreasing and convergent.

Q: So 20 (x? – 1)ª æ dæ = O 2/5 O 20 O 2 O -2 O -20

A: Definition used -                 Definite integral -                 ∫abf(x)dx =F(b)-F(a)…

Q: 8. Prove the following. A. Let X = {a e N|a = 3t + 4, for some t e N} and Y= {a eN | a = 21t + 4,…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.