Question
Consider an infinite series of the form
(+-)3(+-)1(+-)1/3(+-)1/9(+-)1/27(+-)....(+-)1/3^n(+-)...
The number 3,1, etc. are given but you will decide what the signs should be.
a)Can you choose the signs to make the series diverge?
B)Can you choose the signs to make the series sum to 3.5?
c)Can you choose the signs to make the series sum to 2.25?
In each case, if your answer is Yes, then specify how to choose the signs; if your answer is No, then explain
(+-)3(+-)1(+-)1/3(+-)1/9(+-)1/27(+-)....(+-)1/3^n(+-)...
The number 3,1, etc. are given but you will decide what the signs should be.
a)Can you choose the signs to make the series diverge?
B)Can you choose the signs to make the series sum to 3.5?
c)Can you choose the signs to make the series sum to 2.25?
In each case, if your answer is Yes, then specify how to choose the signs; if your answer is No, then explain