Question

Let N be a positive integer. Show that if a_n=b_n for n >= N, then Sum(a_n) and Sum(b_n) either both converge, or both diverge.

Answer 1

@satellite73 can u help, plz?

Answer 2

@imranmeah91 ?

Answer 3

what class is it?

Answer 4

Cal 2

Answer 5

@Zarkon can u take a look at this too?

Answer 6

the sum up to N-1 is a finite sum so it doesn't contribute to the convergence or divergence of the series.

Answer 7

is assume \(\sum a_n\) converges

then \[\sum_{k=1}^{\infty}b_n=\sum_{k=1}^{N-1}b_n+\sum_{k=N}^{\infty}b_n\]

\[=\sum_{k=1}^{N-1}b_n+\sum_{k=N}^{\infty}a_n\]

since \(\sum_{k=1}^{N-1}b_n\) is finite and \(\sum a_n\) converge...so does \(\sum b_n\)

Answer 8

tnx a lot man u're a lifesaver!

Answer 9

np