decide if the following series converges or not. what test?

1)sum from n=1 to infinity 5n(0.1)^n

2) sum from n=1 to infinity 5n/10^n

step by step please

Question

decide if the following series converges or not. what test?

1)sum from n=1 to infinity 5n(0.1)^n


2) sum from n=1 to infinity 5n/10^n



step by step please

experimentx · Answer

#1 5n(0.1)^n or 5x(0.1)^n??
#2 1 and 2 are same

experimentx · Answer

converges http://www.wolframalpha.com/input/?i=integrate+5x%280.1%29^x+from+1+to+infinity

anonymous · Answer

i need steps. Thanks

experimentx · Answer

you know integral test for convergence??

anonymous · Answer

unfortunately, i do not. Help me please...

experimentx · Answer

ratio test??

anonymous · Answer

ah, yes, i know. thanks

anonymous · Answer

However, when i did it i replace n+1 for all of n and then Im completely blank..

experimentx · Answer

http://www.wolframalpha.com/input/?i=lim+n-%3Einf+%285%28n%2B1%290.1^%28n%2B1%29%29%2F%285n%280.1%29^n%29 should be less than 1

anonymous · Answer

alright, thanks a lot.

experimentx · Answer

it's value would be 0.1 < 1 so it must converge