Question

Geometric Series

Answer 1

is \[ \sum_{n=0}^{\infty} 5^{n+2} 3^{-2n}\]

a geometric series? if, so find its initial term a, common ration r and the sum

Answer 2

ratio*

Answer 3

put n=0 to get the first term

Answer 4

here first term is 25

Answer 5

second term is 125/9
so common ratio is (125/9 ) /25 =5/9

Answer 6

how did u get the second term?

Answer 7

@matricked

Answer 8

so thats it for finding the initial term a, common ration r and the sum s?

Answer 9

*ratio

Answer 10

for second term n=1

Answer 11

here r=5/9 < 1
so sum to infinity = first term / (1 - r )

Answer 12

sum= 25/(1-5/9) =225/4

Answer 13

thank you! great help

can you help with this find the sum of the telescoping series using Partial fraction decomposition

\[\sum_{n=1}^{\infty} \frac{ 1 }{ n ^{2} +3^{n} }\]

Answer 14

do i break the denominator into n(n+3) ?

Answer 15

@matricked

Answer 16

no u can't

Answer 17

ok so?

Answer 18

how do i do partial fraction