Discrete Math. Please answer the g-h-i-j? In computerized and in image. Please this is my last question make it upto j? Thank you! 2. Use mathematical induction to prove that the statements are true for every positive integer n.(a) 1+3 + 6 + ...+n (n+1)n (n+1)(n+2)5n (n+1)(b) 5 + 10 + 15 + ..+ 5n(c) 1² + 2³+ ...+n³ = n?(n+1)²%3D4(d) 1* + 2*+...+nª = n(n+1)(2n+1) (3n² +3n=1)%3D30a"-(e) 1+ a + a² +...+ a"-1 =for a + 0, a # 1a-1(f) 32n + 7 is divisible by 8(g) 13" + 6" is divisible by 7(h) 25n+1 + 52n+2 is divisible by 27(i) 72n + 16n - 1 is divisible by 64G) n3 –n is divisible by 3

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Discrete Math. Please answer the g-h-i-j? In computerized and in image. Please this is my last question make it upto j? Thank you!

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 44E

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Question

Discrete Math. Please answer the g-h-i-j? In computerized and in image. Please this is my last question make it upto j? Thank you!

2. Use mathematical induction to prove that the statements are true for every positive integer n.
(a) 1+3 + 6 + ...+
n (n+1)
n (n+1)(n+2)
5n (n+1)
(b) 5 + 10 + 15 + ..+ 5n
(c) 1² + 2³+ ...+n³ = n?(n+1)²
%3D
4
(d) 1* + 2*+...+nª = n(n+1)(2n+1) (3n² +3n=1)
%3D
30
a"-
(e) 1+ a + a² +...+ a"-1 =
for a + 0, a # 1
a-1
(f) 32n + 7 is divisible by 8
(g) 13" + 6" is divisible by 7
(h) 25n+1 + 52n+2 is divisible by 27
(i) 72n + 16n - 1 is divisible by 64
G) n3 –n is divisible by 3

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