Use mathematical induction to prove the following statement: 8"-1 is a multiple of 7 for all nen

with Step-by-step explanation:

We are given that

P(n)=

We have to prove that given statement is a multiple of 7 using mathematical induction for all natural numbers n belongs to N.

Suppose n=1

Then P(1)=8-1=7

Hence, it is a multiple of 7 .Therefore, it is true for n=1

We suppose that it is true for n=k

Then P(k)= is a multiple of 7.

We shall prove that it is true for n=k+1

P(k+1)= is a multiple of 7

LHS=

=

=

=

=  because is a multiple of 7 therefore

=

P(k+1) is a multiple of 7.

Therefore, P(n) is true for all natural numbers belongs to N.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

$119.20

step-by-step explanation:

$372.50 - 60% off is $149. $149-20% off is $119.20