Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2009-04-07 17:49:43

lb
Guest

calculus help!

the sum of the series from 0 to infinity of (1+sin(n))/10^(n)

#2 2009-04-08 06:13:10

Azathoth
Guest

Re: calculus help!

Do u have to find the exact value or just show that it converges?

#3 2009-04-08 06:54:37

LuisRodg
Real Member
Registered: 2007-10-23
Posts: 322

Re: calculus help!

It converges to zero I think.

Offline

#4 2009-04-08 06:57:18

Azathoth
Guest

Re: calculus help!

actually, i've got 10/9 + [10sin(1)]/[101-20cos(1)] big_smile

#5 2009-04-08 07:07:09

Azathoth
Guest

Re: calculus help!

somebody really have to check if this is right, but here is the idea:
∑[1+sin(n)]/10^n=∑1/10^n+∑sin(n)/10^n the first term is clearly 10/9 (it's 1+0.1+0.01+ ....=1.1111....=10/9)
for the second term we write sin(n)=[e^(in) - e^(-in)]/2i so that the sum is [∑(e^(i)/10)^n - ∑(e^(-i)/10)^n]/2i which is 2 geometric series ... so after some calculation I've got [10sin(1)]/[101-20cos(1)]. Hence, the whole answer is 10/9 + [10sin(1)]/[101-20cos(1)].

#6 2009-04-08 07:15:00

LuisRodg
Real Member
Registered: 2007-10-23
Posts: 322

Re: calculus help!

Would help a lot if you put it in latex.

Offline

#7 2009-04-08 07:58:55

Azathoth
Guest

Re: calculus help!

lb sould be able to understand it, I'm sure tongue

Board footer

Powered by FluxBB