anonymous
  • anonymous
The meaning of the decimal representation of a number 0.d1d2d3 . . . (where the digit i is one of the numbers 0, 1, 2, . . ., 9) is that 0.d1d2d3d4 . . . = d1/10 + d2/10^2 + d3/10^3 + d4/10^4 + . . . Show that this series always converges.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Geeze, what grade is this?? ((I do not know the answer.))
anonymous
  • anonymous
This is calculus 2, so its gonna be tricky!
myininaya
  • myininaya
so you are having trouble this converges: sum(1/10^i,i=1..n)? if this sum coverges then sum(di/10^i,i=1..n) should converges i think

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

myininaya
  • myininaya
ratio test we can show it converges absolutely lim |d{n+1}/10^(n+1)|/|d{n}/10^n| n->inf = " |d{n+1}/10^n*10|*|10^n/d{n}| = " 1/10*|d{n+1}/d{n}| the digits can range form 0 to 9 the biggest number that can be in that absolute value thing is 9/1 so 1/10*9=9/10<1 so it converges absolutely
anonymous
  • anonymous
thank you! this helps immensely. I had a solution worked out involving the "r" value being less than one for 9/10^n (geometric series), making it convergent
anonymous
  • anonymous
r being 1/10

Looking for something else?

Not the answer you are looking for? Search for more explanations.