If Arlo were here, I would be mad. If Arlo spoke to me, I would be mad. If Arlo existed, I would be mad. Which is why I pretend he doesn't. When I wake up, I pretend he's not on the bed next to me. When I brush my teeth, I ignore his endless talking. And when I eat breakfast and leave for school, I pretend that he doesn't exist.
"Addi? Adddiiii... Are you being possessed or something?" I pretend I don't hear him, and my jaw tightens. "Addi!" He claps his hands right in my face. I flinch backwards, and I turn to him, angry.
"What could you possibly need to say that you can't tell me after school?" I push his hands away from me, and he begins to laugh. And then talks nonstop again. He even moves his hands as he talks. Up above his head, below. Up, down, and all around. Finally, he pauses, giving my ears a break. He pulls out a bag of cookies before silently offering me one. I take it, but only because he offered it to me, and it would be rude not to take it. Also, if I were still pretending he was non-existent, flying cookies would not be real. Not because I actually wanted it.
Arlo and I have every class together. Mrs. Plum, the school counselor, put us in the same classes because Arlo asked her to with a "Pretty please!" and twenty dollars. I hate being in the same classes with him. Which, in theory, should be pretty obvious if all I talk about is how much I hate him, but apparently not, because Mika, my best friend, and all of her many friends (she's a popular girl according to herself...) think that I love being in the same classes as Arlo. I do not. And unfortunately, while walking to first period with Mika, I unfortunately... Ran into Arlo. He waves energetically. Almost too energetic. Like as if he was being controlled or was fake or something... But I know that's just his nature. He's weird, like Erica, my mom. And Kenji, my dad...
"Addi! Hey! Where are you going?" Arlo catches up to me, and I try not to show my disappointment. I hate even having to converse with him. Mika is still on the other side of me, smirking. She knows I hate him, and yet she still invites him into the conversation, like she wants him to join. Or make me miserable.
"Oh! Hey, Arlo. Your sister and I were just about to head to math, right, Addi?" She playfully punches my shoulder, and I slowly deflate. Arlo nods as if she was only just catching him up, and then he talks. A lot. Until we get to class. Even as we sit at our desks. Even as the teacher, Ms. Mauling, says, "Quiet down, class!" He just talks and talks and talks and talks...
And talks... And talks... And talkkssssss......
And, unfortunately, when he talks, I can't focus. I can barely hear what Ms. Mauling is saying, and as she passes out papers, and she tells us the instructions. I almost completely zone out before I hear my name, loud and bullet-like.
"Ms. Addison?" I jump at the sound of my name and turn my head towards the front of the class. Fast energy bolts through me as I figure out how the heck am I going to answer. Should I be snobby, or just answer like a good student? Or maybe smart, to get Ms. Mauling angry. There's a reason why she's just Miss Mauling, after all. "Addison!" This time it's demanding. She drops a huge textbook right next to me to snap me out of my thinking.
"Y-yes, Ms. Mauling...?" I slap myself internally for sounding so scared and frail. I hear other children in the class giggling and snickering. And I know why.
"Would you mind answering question four? If you were listening, of course, you would know the answer." I scan the board and find it. Question four.
Compute the exact value of the infinite sum.
S = ∑(n=1 to ∞) 1/[n(n+1)]
I try not to seem overwhelmed as I calculate this in my brain.
We rewrite 1 in (n+1)=An+Bn+1.
So... 1=A(n+1)+Bn=(A+B)n+A.
Match coefficients:
For n: A+B=0
Constant: A=1
So, A=1, B=−1, and
1n(n+1)=1n−1n+1.
S =∑n=1∞(1n−1n+1).
Write the first several:
S=(11−12)+(12−13)+(13−14)+(14−15)+⋯
Everything cancels except the very first 1:
−12 cancels with +12
−13 cancels with +13
−14 cancels with +14
and so on…
So, in the limit, all the middle terms vanish, and we’re left with
S=1.
"The answer is S equals one." The room goes silent. Ms. Mauling pulls out her phone to check it on her calculator. A couple of students turn to me, jaw dropped. Did I do it wrong? What if I got the answer completely wrong and everyone is trying their best not to laugh? I hear her curse under her breath before the first bell rings, and Arlo and I wave Mika goodbye before going to our next class, embarrassed.
ns216.73.216.134da2
and then Add to home screen.