Let

f(x)=(x-1)^(10),p=1

, and

p_(n)=1+(1)/(n)

. Show that

|f(p_(n))|

whenever

n>1

but\ that

|p-p_(n)|

requires that

n>1000

.\ Answer:\ For

n>1

,\

|f(p_(n))|=((1)/(n))^(10)

\ so\

|p-p_(n)|=(1)/(n)1000

. Please show all work neatly :) Answer is provided !

20. Let f(x)=(x1)10,p=1, and pn=1+1. Show that f(pn)1 but that ppn1000. Answer: 20. For n>1, f(pn)=(n1)10(21)10=10241