Mathematics
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OpenStudy (anonymous):
Evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10..
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OpenStudy (anonymous):
does anyone know this.. help
OpenStudy (science0229):
So, you can write this question as \[\sum_{n=2}^{10}25*0.3^n*0.3=\sum_{n=2}^{10}7.5*0.3^n\]
OpenStudy (science0229):
We can write that as \[7.5*0.3^2+7.5*0.3^3+...+7.5*0.3^10\], right?
OpenStudy (science0229):
Correction: The last term is supposed to be 7.5*0.3^10
OpenStudy (anonymous):
no this is not right
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OpenStudy (science0229):
Why not?
OpenStudy (anonymous):
Evaluate the summation of negative 2 n minus 3, from n equals 2 to 10. then how do u do this in sigma notation
OpenStudy (science0229):
\[\sum_{n=2}^{10}(-2n-3)\]
OpenStudy (anonymous):
yes!!!!!! thankyou how do you solve this
OpenStudy (science0229):
There is a sigma property.
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OpenStudy (science0229):
\[\sum_{x=a}^{b}(nx+m)=n \sum_{x=a}^{b}x+\sum_{x=a}^{b}m\]
OpenStudy (science0229):
a,b,n,m are all constants
OpenStudy (anonymous):
okay how do u solve the one i gave you... my answer choices are
-270
-135
135
270
OpenStudy (science0229):
You mea the second one?
OpenStudy (anonymous):
yes that one
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OpenStudy (science0229):
First, use the sigma property I gave you to get this
OpenStudy (science0229):
\[-2\sum_{n=2}^{10}n-\sum_{n=2}^{10}3\]
OpenStudy (anonymous):
can you show me please
OpenStudy (science0229):
On what part do you need help on?
OpenStudy (anonymous):
i got 135 but i dont think its right
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OpenStudy (science0229):
First, do you know how to calculate \[\sum_{n=2}^{10}n\]
OpenStudy (anonymous):
no i really dont. i just learned this
OpenStudy (science0229):
Ok.
OpenStudy (science0229):
If you expand that, you get 2+3+4+5+6+7+8+9+10
OpenStudy (anonymous):
okay i got that idk what to do afterwards
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OpenStudy (science0229):
2+3+4+5+6+7+8+9+10=A
10+9+8+7+6+5+4+3+2=A
12+12+12+12+12+12+12+12+12=2A
12*9=2A
54=A
OpenStudy (science0229):
So, \[\sum_{n=2}^{10}n=54\]
OpenStudy (anonymous):
im confussed bc thats not the answer to my problem :(
OpenStudy (science0229):
Going back to what I previously said, we said that \[\sum_{n=2}^{10}(-2n-3)=-2\sum_{n=2}^{10}n-\sum_{n=2}^{10}3\]
OpenStudy (science0229):
We found that \[\sum_{n=2}^{10}n=54\]
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OpenStudy (anonymous):
Evaluate the summation of 3 n plus 2, from n equals 1 to 14..
39
49
340
343
OpenStudy (science0229):
So, the 1st equation becomes \[-2(54)-\sum_{n=2}^{10}3=-108-\sum_{n=2}^{10}3\]
OpenStudy (science0229):
\[\sum_{n=2}^{10}3=3*9=27\]
OpenStudy (science0229):
So, the 2nd equation becomes -108-27, which is -135
OpenStudy (science0229):
So,\[\sum_{n=2}^{10}(-2n-3)=-135\]
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OpenStudy (anonymous):
okay i got that !!!!!
OpenStudy (anonymous):
Evaluate the summation of 3 n plus 2, from n equals 1 to 14. how you do this one
OpenStudy (science0229):
Try it on your own.
I'll help if you're stuck.
You can show work on here.
OpenStudy (anonymous):
okay so do i do the 1+2+3+4 thing
OpenStudy (anonymous):
im not good at this
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OpenStudy (science0229):
After that problem, I'll tell you a shortcut to these kind of problems.
OpenStudy (anonymous):
okay thankyou. im sorry to give you all this trouble
OpenStudy (anonymous):
so do i do the 1+2+3 thing
OpenStudy (science0229):
Ok.
OpenStudy (anonymous):
what do i do now?
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OpenStudy (science0229):
What did you do so far?