Question

Write the expanded series represented by the given summation notation.

Answer 1

\[\sum_{b=3}^{7} (\frac{ 1 }{ b^2-2 })\]

Answer 2

\[\frac{ 1 }{ 3^2-2 }+\frac{ 1 }{ 6^2-2 }+\frac{ 1 }{ 9^2-2 }+\frac{ 1 }{ 12^2-2 }\frac{ 1 }{ 15^2-2 }+\frac{ 1 }{ 18^2-2 }+\frac{ 1 }{ 21^2-2 }\]

Answer 3

not quite

Answer 4

The b=3 signifies the number you start at, while 7 signifies where you end.

Answer 5

i know we start at three, then if the expanded form isnt correct, then what will it be

Answer 6

As it is now, you are starting at 3, going to 21 by increments of 3. Instead you go by increments of 1 up to the end of 7.

Answer 7

then it would be 3,4,5,6,7,

Answer 8

Yes, that's what b would equal in each, then you sum them all together.(Hence summation notation)

Answer 9

@heril it will become \[\frac{ 1 }{ 7 }+\frac{ 1 }{ 14 }+\frac{ 1 }{ 23 }+\frac{ 1 }{ 34 }+\frac{ 1 }{ 47 }\]

Answer 10

but if the denominators are not the same we cannot add them

Answer 11

You can add them, you just need to work them to get a common denominator. That answer matches what I got.

Also, the question asks for the expanded series. I assume you don't have to actually add them up then.

Answer 12

okay

Answer 13

@heril \[\sum_{j=0}^{4} (5)=\] what would be the expanded form of this equation

Answer 14

You go about it much the same way, except your starting and end point are different and your function is very different.