1. ## sequence help

Let an be the $\displaystyle a_n$ th digit after the decimal point in
7$\displaystyle pi$+2e . Evaluate
$\displaystyle \sum_{n=1}^\infty a_n (.1)^n.$

can someone show me how to solve this.

2. Trick question.

The answer is $\displaystyle 7 \pi + 2 e$.

3. Originally Posted by dat1611
Let an be the $\displaystyle a_n$ th digit after the decimal point in
7$\displaystyle pi$+2e . Evaluate
$\displaystyle \sum_{n=1}^\infty a_n (.1)^n.$

can someone show me how to solve this.
Should be your question like this:
Let $\displaystyle a_n$ be the $\displaystyle n$ th digit after the decimal point in $\displaystyle 7\pi+2e$ . Evaluate $\displaystyle \sum_{n=1}^\infty a_n (.1)^n.$

If so, the result would be $\displaystyle 7\pi+2e-\lfloor 7\pi+2e \rfloor$

4. Yes I agree - sorry, ignore my first answer, you need to subtract the integer part from it like Luobo has done.

It's still a trick question!

5. is not the correct answer though

6. Originally Posted by dat1611
Let an be the $\displaystyle a_n$ th digit after the decimal point in
7$\displaystyle pi$+2e . Evaluate
$\displaystyle \sum_{n=1}^\infty a_n (.1)^n.$

can someone show me how to solve this.
"Let an be the $\displaystyle a_n$ th digit after the decimal point in 7$\displaystyle pi$+2e"

What do you mean by this? Does this make any sense?

You need make your problem clear and correct so that others can help you correct. Do not let people GUESS what you mean.

7. Originally Posted by luobo
"Let a_n be the $\displaystyle a_n$ th digit after the decimal point in 7$\displaystyle pi$+2e"

What do you mean by this? Does this make any sense?

You need make your problem clear and correct so that others can help you correct. Do not let people GUESS what you mean.
its supposed to be "Let $\displaystyle a_n$ be the nth digit after the decimal point in 7$\displaystyle pi$+2e"

8. Okay, so what *is* the correct answer?

$\displaystyle 7 \pi + 2 e - \lfloor {7 \pi + 2 e}\rfloor$ looks fine to me.

9. Originally Posted by Matt Westwood
Okay, so what *is* the correct answer?

$\displaystyle 7 \pi + 2 e - \lfloor {7 \pi + 2 e}\rfloor$ looks fine to me.
what do these mean $\displaystyle \lfloor \rfloor$