SOLUTION: Does the infinite series diverge or converge? If it converges what is the sum? 10+2+2/5+2/25+.... what is a_n= 2a_n-1 -1 where a

SOLUTION: Does the infinite series diverge or converge? If it converges what is the sum? 10+2+2/5+2/25+.... what is a_n= 2a_n-1 -1 where a_1 = 2? Thank you !!!

Question 1001038: Does the infinite series diverge or converge? If it converges what is the sum?
10+2+2/5+2/25+....
what is
a_n= 2a_n-1 -1 where a_1 = 2?
Thank you !!!
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
Does the infinite series diverge or converge? If it converges what is the sum?
10+2+2/5+2/25+....
---------------------------------------------------------

It is the sum a geometric progression with the first term a = 10 and the common ratio r = .

This infinite series converges for any geometric progression with the common ratio less than 1 in the modulus.

The sum of an infinite geometric progression with the first term a and the raio r, |r| < 1, is

S = .

In your case S = = = = 12.5.

----------------------------------------------------------
what is
a_n= 2a_n-1 -1 where a_1 = 2?
----------------------------------------------------------

= 2
= = 2*2 - 1 = 3,
= = 2*3 - 1 = 5,
= = 2*5 - 1 = 9,
= = 2*9 - 1 = 17,
and so on . . .

You can easily calculate it yourself.

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