5) Prove by induction. For every integer n 23, 5(5" - 25) 5° +54 + ..............
Prove using mathematical induction that for every integer n > 4, 2^n > n^2.
Prove using mathematical induction that for every positive integer n, = 1/i(i+1) = n/n+1. 2) Suppose r is a real number other than 1. Prove using mathematical induction that for every nonnegative integer n, = 1-r^n+1/1-r. 3) Prove using mathematical induction that for every nonnegative integer n, 1 + i+i! = (n+1)!. 4) Prove using mathematical induction that for every integer n>4, n!>2^n. 5) Prove using mathematical induction that for every positive integer n, 7 + 5 + 3 +.......
Prove using the Basic Principle of Mathematical Induction: For every positive integer n 24 | (5^(2n)- 1)
Problem 5.1.3. Prove by induction on n that (1+ n < n for every integer n > 3.
Use mathematical induction to prove that the statement is true for every positive integer n. 5n(n + 1) 5 + 10 + 15 +...+5n = 2
R->H 7. Prove by induction that the following equation is true for every positive integer n. (4 Points) 1. 4lk11tl + 2K ²+ 3k 4k+4+H26² +3k {(4+1) = (40k41) 40) j=1 (4i + 1) = 2 n 2 + 3n 2K?+75 +5 21 13 43 041) 262, ultz
Prove by induction that for every positive integer n, the following identity holds: 1+3+5+...+(2n – 1) = np. Stated in words, this identity shows that the sum of the first n odd numbers is n’.
n(n+1)(n+2) for every posi- 7. Use mathematical induction to prove that tive integer n.
Write as a complete proof. P19,9. Use induction to prove that for every positiveinteger n, 5 s an integer. 3 5 15
Use mathematical induction to prove that the statements are true for every positive integer n. 1 + [x. 2 - (x - 1)] + [ x3 - (1 - 1)] + ... + x n - (x - 1)] n[Xn - (x - 2)] 2 where x is any integer 2 1