- #1

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how can I prove that if A is a converges and B diverges

that the Sum of these series (A +B) diverges..

( A = a1 + a2 + a3 + ...

B = b1 + b2 + b3 + ...) if the series start from n=1

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- Thread starter mrnoll
- Start date

- #1

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how can I prove that if A is a converges and B diverges

that the Sum of these series (A +B) diverges..

( A = a1 + a2 + a3 + ...

B = b1 + b2 + b3 + ...) if the series start from n=1

- #2

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The convergence of the series is determined by the row of partial sums.

Therefore, if both rows converge, the sum of both will too.

- #3

HallsofIvy

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- #4

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I dont think it´s that easy actually.

Because what I forgot to say was that these series go from

n=1 to n=infinity.

And in infinity normal rules dont always apply like SumA + SumB = Sum(A+B)

I need a proof... :)

- #5

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- #6

HallsofIvy

Science Advisor

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I dont think it´s that easy actually.

Because what I forgot to say was that these series go from

n=1 to n=infinity.

And in infinity normal rules dont always apply like SumA + SumB = Sum(A+B)

In this case they do. If Sum(A) and Sum(B) exist then

Sum(A+ B) exists and is equal to Sum(A)+ Sum(B).

I had assumed you were talking about infinite series since otherwise it wouldn't make sense to talk about "convergent" and "divergent".

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