Question

Sequences.

Answer 1

how is this answer "1/3" this was the instructions..

Answer 2

"Determine whether the series converges, and if so find its sum."

Answer 3

i found the ratio to be 3/5 by doing
r= (1/20)/(1/12)
Then found the sum by
S= (1/12) / (1 - (3/5) )

Answer 4

I got 5/24 :/

Answer 5

I just barely realized it is not a geometric series but I'm still not sure how they got the answer

Answer 6

haha cool :)

Answer 7

try below :

1/(k+2)(k+3) = 1/(k+2) - 1/(k+3)

Answer 8

will telescoping work ?

Answer 9

Curious: Have you heard of "telescoping series?" or of "partial fraction expansions?"

Answer 10

aw darn yes i have actually

Answer 11

I think your best bet would be to re-write 1 / [(k+2)(k+3) ] in its partial fraction expansion. If you do this correctly, you'll find that all the middle terms cancel out, leaving you only with the very first and the very last term. Does this sound at all familiar?

Answer 12

The cancelling middle terms are what lead us to call this a "telescoping series."

Answer 13

If you choose to experiment with partial fractions, please find A and B in the following?\[\frac{ 1 }{ (k+2)(k+3) }=\frac{ A }{ k+2 }+\frac{ B }{ k+3 }\]

Answer 14

If done correctly, this will result in the following:

1/3 - 1/4 + 1/4 - 1/5 +1/5 -1/6 + ......

what is -1/4 = 1/4? -1/5 + 1/5? and so on. What's left on the far left end of this series?

Answer 15

Please note that ganeshie8 has already done much of the work for you. See his formula, above.

Answer 16

thank you both!!