Question

72n + 23n-3.3n-1 is divisible by 25.
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Answer 1

Answer:

hope this helps u

Step-by-step explanation:

first process:

7²ⁿ + 2³ⁿ.3ⁿ⁻¹

= (7²)ⁿ + (2³)ⁿ⁻¹. 3ⁿ⁻¹

= 49ⁿ  + 8ⁿ⁻¹.3ⁿ⁻¹

= (49)ⁿ + (8.3)ⁿ⁻¹

= 49ⁿ + 24ⁿ⁻¹

= (50-1)ⁿ + (25-1)ⁿ⁻¹

= 50ⁿ -n.50ⁿ⁻¹ + ....+(-1)ⁿ⁻¹. n50 +(-1)ⁿ] + [25ⁿ⁻¹ - n.25ⁿ⁻²+.... + (-1)ⁿ⁻². (n-1).25 +(-1)ⁿ⁻¹]

divide the whole equation by 25

we get

(-1)ⁿ +  (-1)ⁿ⁻¹ = 0

we can conclude P(n) is true for all  n∈N