Finding the sum of series using integral test

[Salman Ali]

So this is the question. But we cannot apply integral test because the function is not positive. Isn't it so? So what formula will be used. Also, I am very confused that when to use which formula.

 

[MarkFL]

The integral test is a test for convergence, but won't necessarily give you the value of the series. I would treat this series as telescoping to find the infinite sum.

 

[Jagulba]

did they ask you to use integral or integral test? can you solve it without integral?

 

[Salman Ali]

I have to use integral test!

did they ask you to use integral or integral test? can you solve it without integral?

 

[pka]

View attachment 13445
So this is the question. But we cannot apply integral test because the function is not positive. Isn't it so? So what formula will be used. Also, I am very confused that when to use which formula.

Sometimes there are mistakes in instructions that accompany printed problems.
This is clearly such a case. Look at this link.

 

[Dr.Peterson]

Reread post #2. The integral test will not find the sum.

Please state the entire problem (with instructions) exactly as given to you. Did it really say to find the sum, or just to test for convergence?

But also, why do you say "the function is not positive"?

 

[Jagulba]

View attachment 13445
So this is the question. But we cannot apply integral test because the function is not positive. Isn't it so? So what formula will be used. Also, I am very confused that when to use which formula.

for n>=1 ,do you think the following statement is correct or not:
2ⁿ>2ⁿ⁺¹