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Setler [38]
3 years ago
7

-4 ( 6 - 2n ) = 30 + 8n Please help me

Mathematics
1 answer:
pogonyaev3 years ago
3 0
N = no solution

-4 ( 6 - 2n ) = 30 + 8n
-24 + 8n = 30 + 8n
Subtract 8n from both sides
-24 = 30
This is invalid therefore no solution
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Answer:

The series converges to   $ \frac{1}{1-9x} $     for   $ \frac{-1}{9} < x < \frac{1}{9} $                

Step-by-step explanation:

Given the series is     $ \sum_{n=0}^{\infty} 9^n x^n $

We have to find the values of x for which the series converges.

We know,

$ \sum_{n=0}^{\infty} ar^{n-1} $ converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, $ \sum_{n=0}^{\infty} 9^n x^n =  \sum_{n=0}^{\infty} (9x)^{n}  $ is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for $ \frac{-1}{9} < x < \frac{1}{9} $

And geometric series converges to $ \frac{a}{1-r} $

Here, a = 1 and r = 9x

Therefore, $ \frac{a}{1-r} = \frac{1}{1-9x} $

Hence, the given series converges to   $ \frac{1}{1-9x} $     for   $ \frac{-1}{9} < x < \frac{1}{9} $

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