Question

PROOF BY INDUCTION HELP PLZ!!
http://puu.sh/bTJQ3/402ed736ee.png

Answer 1

@iambatman help please :S

Answer 2

@gorv

Answer 3

for n=1

Answer 4

do i have to do induction for k AND n? (since there are 2 variables..)

Answer 5

no only one we hake to check

Answer 6

first for n=1
than n=k
and than n=k+1

Answer 7

either one?

Answer 8

all 3we have to test ...

Answer 9

so it's a long induction proof..?

Answer 10

yeah :P

Answer 11

thanks ill try

Answer 12

for n=1
K+1>=K+1 true
now let for n=k
(k+1)^k>= 1 +k*K

Answer 13

now for n=k+1
(k+1)^(k+1)>=1+k*(k+1)
(k+1)^(k+1)>=1+k^2+k
((k+1)^k)(k+1)>=1+k^2+k
we considered
k+1)^K>=1+k*k
so
((k+1)^k)(k+1) >=1+k^2+k

Answer 14

n=1 :
(1+k)^1 >= 1+k*1 true

assume (1+k)^n >= 1+kn for some n

multiply both sides by (1+k) :
(1+k)(1+k)^n >= (1+k)(1+kn)
(1+k)^(n+1) >= 1+k + kn + k^2n
>= 1 + (n+1)k + k^2n
>= 1 + (n+1)k