Evaluate the limit of the sequence

[gkamal]

Homework Statement

[/B]

Homework Equations

delta(x) = [b-a]/n
xi=a+delta(x)i

The Attempt at a Solution

So, it is said that i have to use riemann sums to solve this one.
what i did is i took the 1/12k out thus getting

1/12k[1/[1+1/12k] + 1/[1+2/12k] + 1/{1+19k/12k]]

I found that

xi = 1+1/12k
so ,
b-a = 1/12 and since a=1 b=13/12

i find that f(x) = 1/x and i evalute the integral from 1 to 12/12 of 1/x

I keep getting the wrong answer i really don't know what to do anymore

 

[Mark44]

Homework Statement

[/B]

Homework Equations

delta(x) = [b-a]/n
xi=a+delta(x)i

The Attempt at a Solution

So, it is said that i have to use riemann sums to solve this one.
what i did is i took the 1/12k out thus getting

1/12k[1/[1+1/12k] + 1/[1+2/12k] + 1/{1+19k/12k]]

This isn't right. Above you show three terms.
b₁ is a sum that contains 8 terms. How many terms are there in b₂? b₃? b_n?

I found that

xi = 1+1/12k
so ,
b-a = 1/12 and since a=1 b=13/12

i find that f(x) = 1/x and i evalute the integral from 1 to 12/12 of 1/x

Since 12/12 = 1, the integral is $\int_1^1 \frac 1 x dx = 0$.

I keep getting the wrong answer i really don't know what to do anymore

 

[gkamal]

This isn't right. Above you show three terms.
b₁ is a sum that contains 8 terms. How many terms are there in b₂? b₃? b_n?
Since 12/12 = 1, the integral is $\int_1^1 \frac 1 x dx = 0$.

i found the answer already but still thanks btw the 12/12 was a typo obviously since the b found on the line before was 13/12