I need help on a series question! ?

Question

Let a(sub n) be the n th digit after the decimal point in 6pi+2e. Evaluate

sigma (a(sub n)(.1)^n. n=1 to inf.

help please!

Answer 1

Question is not quite clear.

I can do this..Just evolve it to make it clear.

If I can understand the question, then I can help you out!

Answer 2

Obviously, the answer is 6*Pi+2*e-[6*Pi+2*e], where

[.] stands for the entier function (i.e. integer part).

Since Pi is approx =3.14 and

e is approx =2.71, then

[6*Pi+2*e]=24

So the answer is 6*Pi+2*e-24

Here's why:

It's known that both Pi and e are irrational and moreover, transcendental numbers. They are represented by decimal numbers with infinitely many decimal digits.

Suppose 6*Pi+2*e=24.a1a2a3... is the representation.

Then your series is equal to a1*0.1+a2*0.01+

+a3*0.001+...=0.a1a2a3...=

=6*Pi+2*e-24