sequence help

**dat1611** · August 13th 2009, 12:02 PM

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

can someone show me how to solve this.

**Matt Westwood** · August 13th 2009, 01:17 PM

Trick question.

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

Think about it.

**luobo** · August 13th 2009, 02:52 PM

Originally Posted by dat1611

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

can someone show me how to solve this.

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

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

If not, please clarify.

**Matt Westwood** · August 13th 2009, 09:30 PM

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!

**dat1611** · August 18th 2009, 07:00 AM

is not the correct answer though

**luobo** · August 18th 2009, 03:22 PM

Originally Posted by dat1611

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

can someone show me how to solve this.

"Let an be the $a_n$ th digit after the decimal point in 7 $pi$ +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.

**dat1611** · August 19th 2009, 10:17 AM

Originally Posted by luobo

"Let a_n be the $a_n$ th digit after the decimal point in 7 $pi$ +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 $a_n$ be the nth digit after the decimal point in 7 $pi$ +2e"

**Matt Westwood** · August 19th 2009, 11:11 AM

Okay, so what *is* the correct answer?

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

**dat1611** · August 19th 2009, 11:27 AM

Originally Posted by Matt Westwood

Okay, so what *is* the correct answer?

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

what do these mean $\lfloor \rfloor$

**Matt Westwood** · August 19th 2009, 09:26 PM

Floor function:

Floor and ceiling functions - Wikipedia, the free encyclopedia

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