Use math induction to prove V n E N, P(n) is true, where P(n) is the claim + (2n – 1) (2n + 1) + (2n + 3) + .…· (4n – 1) 1 + 3 +5 + 1 ... 3 -

pn+1 – 1 1. Use the formula 1+r +r² + .. + r" to evaluate the quantity r – 1 2+4+8+. + 4096 ... 2. Prove by induction that (п — 2)(п + 3) 3+4+5+... +n =

n(n+1)(2n+1) 2. Prove the following using induction: 1+ 4+ 9+ · ..+n² 6

3. Answer any one of 3(a) and 3(b). (a) Use mathematical induction to prove the following inequality: 4n > 1+ 3n for all positive integers n. (b) Prove that E, i (2²-1) = (n – 1)2" + 1 for all positive integers n using mathematical induction.

Establish the formulos below induction. by mothemotical +3+5tt(2n-1)=n(2n-D (2nt) for all nz I

Use linear combination definition: ma+nb= 1

4. Prove that n(3n – 1)r x + 4x + 7x +.. + (3п - 2)x for n e N.

6) Prove by Mathematical Induction the statement that 1+5+9+…+ (4n – 3) = n(2n – 1)