If n is a natural number, then 6^ n– 5^ n
always ends with :-
a) 1 b) 3 c) 5 d) 7.
prove your answer.
urgent please send answer fast
Answers
Answered by
71
Case 1 :- Let n is an even number .
n = 2, 4 , 6, 8, 10, 12 ..........
now,
take n = 2
6² - 5² = 36 -25 = 11 ends with 1
take n = 4
6³ - 5³ = (6)⁴ - (5)⁴
= (6² + 5)²( 6² -5²)
= (36 +25)( 6 -5)(6+5)
= 61 × 1 × 11 hence ends with 1
..............
......,....
hence, if we take n is an even number then, 6^n - 5^n ends with 1
Case2 :- Let n is an odd number .
n = 1, 3 , 5 , 7, 9, 11...........
take n = 1
6¹ - 5¹ = 6 -5 = 1 ends with 1
take n = 3
6³ - 5³ = (6 -5)(6² + 5² + 6×5)
= 11 × ( 36 +25 +30)
= 11 × 91 ends with 1
,..................
................
hence, if we take n Is an odd number then 6^n - 5^n also ends with 1.
now , by case1: and case2: we conclude that 6^n -5^n ends with 1 when n is a natural number .
so, option (a ) is correct .
n = 2, 4 , 6, 8, 10, 12 ..........
now,
take n = 2
6² - 5² = 36 -25 = 11 ends with 1
take n = 4
6³ - 5³ = (6)⁴ - (5)⁴
= (6² + 5)²( 6² -5²)
= (36 +25)( 6 -5)(6+5)
= 61 × 1 × 11 hence ends with 1
..............
......,....
hence, if we take n is an even number then, 6^n - 5^n ends with 1
Case2 :- Let n is an odd number .
n = 1, 3 , 5 , 7, 9, 11...........
take n = 1
6¹ - 5¹ = 6 -5 = 1 ends with 1
take n = 3
6³ - 5³ = (6 -5)(6² + 5² + 6×5)
= 11 × ( 36 +25 +30)
= 11 × 91 ends with 1
,..................
................
hence, if we take n Is an odd number then 6^n - 5^n also ends with 1.
now , by case1: and case2: we conclude that 6^n -5^n ends with 1 when n is a natural number .
so, option (a ) is correct .
Anubhav76:
thankyou very much
Answered by
19
Answer:
Your answer is 1
Step-by-step explanation:
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