Question

(2x3n-1) is divisible by 7 prove by method of induction, for all neN​

Answer 1

Step-by-step explanation:

Setting n=1

8×1−1=7

above number is divisible by 7 for n=1

assume that 8n−1 is divisible by 7 for n=k then

8k−1=7m

or

8k=7m+1(1)

where, m is some integer

setting n=k+1,

8k+1−1

=8⋅8k−1

setting the value of 8k from (1),

=8(7m+1)−1

=7(8m+1)

since, (8m+1) is an integer hence the number 7(8m+1) is

divisible by 7 thus 8n−1 is divisible by 7 for n=k+1

hence, 8n−1 is divisible by 7 for all integers n≥1