3/8n + 1 = –25 What is the number for n?
Answers
Answer:
If a number is divisible by 8
16=8×2
24=8×3
64=8×8
Any number divisible by 8=8×Natural number
Let P(n):3
2n+2
−8n−9=8d where d∈N
For n=1
L.H.S=3
2×1+2
−8×1−9
=81−17=64=8×8=R.H.S
∴P(n) is true for n=1
Assume P(k) is true.
3
2k+2
−8k−9=8m where m∈N (1)
P(k+1):3
2(k+1)+2
−8(k+1)−9
=9(3
2k+2
)−8k−17
=9(8k+9+8m)−8k−17
=72k+81+72m−8k−17
=64k+64+72m
=8(8k+8+9m)=8r where r=8k+8+9m is a natural number.
∴P(k+1) is true whenever P(k) is true
∴ By the principle of mathematical induction, P(n) is true for n where n is a natural number.
Answer:
Answer:
If a number is divisible by 8
16=8×2
24=8×3
64=8×8
Any number divisible by 8=8×Natural number
Let P(n):3
2n+2
−8n−9=8d where d∈N
For n=1
L.H.S=3
2×1+2
−8×1−9
=81−17=64=8×8=R.H.S
∴P(n) is true for n=1
Assume P(k) is true.
3
2k+2
−8k−9=8m where m∈N (1)
P(k+1):3