This hypothesis is right about operators on convergent and divergent series?

[MAGNIBORO]

Sorry for the bad English , do not speak the language very well.
I posted this to know if the statement or " hypothesis " is correct .

thank you very much =D.

First Image:https://gyazo.com/7248311481c1273491db7d3608a5c48e
Second Image:https://gyazo.com/d8fc52d0c99e0094a6a6fa7d0e5273b6
Third Image:https://gyazo.com/035813f059d3eb7bb4131af7cd8f29c3

 

[micromass]

No, it isn't correct. Learn about convergent and divergent series, and which operations are allowed on them. You need to be very careful with convergence issues.

 

[MAGNIBORO]

No, it isn't correct. Learn about convergent and divergent series, and which operations are allowed on them. You need to be very careful with convergence issues.

the error is on the part of the two match series with a formula? ( image 2 )

 

[micromass]

the error is on the part of the two match series with a formula? ( image 2 )

The error is assuming the series converges and thus can be treated as real numbers instead of infinity.

 

[MAGNIBORO]

The error is assuming the series converges and thus can be treated as real numbers instead of infinity.

thanks