What does Brutus think of the letter in Julius Caesar?

Brutus gets a letter asking him to strike Caesar and it apparently convinces him to go through with the assasination.

Cassius approaches Brutus at the feast of Lupercal and tells him that Julius Caesar is too ambitious and powerful. A group of men have gotten together to assassinate Caesar. This is obviously a very dangerous move. They need Brutus to join their conspiracy in order to lend it legitimacy.

CASCA

O, he sits high in all the people's hearts:
And that which would appear offence in us,
His countenance, like richest alchemy,
Will change to virtue and to worthiness. (Act 1, Scene 3)

About a month later, the day before the attack, Brutus ponders Caesar’s fate in a soliloquy. He determines that while Caesar has not done anything wrong now, he should act before the man gets so powerful that they can’t stop him.

After Brutus has this little talk with himself, his servant Lucius brings him a letter. Lucius explains that he found it in the windowsill.

The taper burneth in your closet, sir.
Searching the window for a flint, I found
This paper, thus seal'd up; and, I am sure,
It did not lie there when I went to bed. (Act 2, Scene 1)

Mysterious! Apparently the conspirators are still courting Brutus. They want to make sure he does not change his mind. They decided to leave letters for Brutus urging him to join, written in several different handwritings so that Brutus will think that there is a huge popular movement to get him to kill Caesar.

Cassius tells Cinna to leave the paper where Brutus will find it. He knows how impressionable and conceited Brutus is, and is engaging in a multi-legged campaign to convince Brutus to lend his name to their cause.

Brutus takes the letter seriously.

Am I entreated
To speak and strike? O Rome, I make thee promise:
If the redress will follow, thou receivest
Thy full petition at the hand of Brutus! (Act 2, Scene 1)

It clearly works. The letter, which says, “Speak, strike, redress!” is a little confusing to Brutus at first, but he determines that it means that the people are against Caesar and he should take action against him as soon as possible.  Of course, it is the day before the Ides of March, so opportunities to back out are not plentiful.

Cassius is very clever in manipulating Brutus. Brutus is full of ego and considers himself honorable. He really is convinced that he is doing what is best for Rome. Although he is conflicted because he is killing someone who is like a father to him, ultimately his distorted sense of duty wins out. Brutus really does think he is doing the right thing.