etc..

(the sequence consists only from positive number so the sum is not negative)

in order to prove that its convergent i need to prove monotonicity and boundedness

monotonicityby induction)

so i guess its increasing

suppose n=k is true:

prove n=k+1 ( )

i proved the opposite

so this is weird.

the answer in the book tells me to split the sequence into odd /even sub sequences

the one is ascending and the other its descending.

i cant see how many sub sequences i need to split it to

maybe its 5 or 10

what is the general way of solving it.

and how you explained that i proved the opposite