Mixing
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangle
$begingroup$
This is regarding "using Integral Bounds to Estimate the Sum of a Series"
I do understand the proof for the integral test. However not as my book explains it.
So consider the expression below:
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangle
how does the limit s subtracted by the general expression for the reimann sum $s_{n}$ equal the sum of areas of a rectangle?
I do understand that a riemann sum for $a_{n}$ with a width of 1 gives me the area of each rectangle.
But
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangles
is lost on me.
integration convergence
asked Jan 7 at 22:50
oxodooxodo
32219
$endgroup$
add a comment |
$begingroup$
This is regarding "using Integral Bounds to Estimate the Sum of a Series"
I do understand the proof for the integral test. However not as my book explains it.
So consider the expression below:
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangle
how does the limit s subtracted by the general expression for the reimann sum $s_{n}$ equal the sum of areas of a rectangle?
I do understand that a riemann sum for $a_{n}$ with a width of 1 gives me the area of each rectangle.
But
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangles
is lost on me.
integration convergence
asked Jan 7 at 22:50
oxodooxodo
32219
$endgroup$
$begingroup$
I think you'll need to write out the proof in your book, because it's impossible to follow this logic without some wider context.
$endgroup$
– Theo Bendit
Jan 7 at 23:12
add a comment |
$begingroup$
This is regarding "using Integral Bounds to Estimate the Sum of a Series"
I do understand the proof for the integral test. However not as my book explains it.
So consider the expression below:
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangle
how does the limit s subtracted by the general expression for the reimann sum $s_{n}$ equal the sum of areas of a rectangle?
I do understand that a riemann sum for $a_{n}$ with a width of 1 gives me the area of each rectangle.
But
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangles
is lost on me.
integration convergence
asked Jan 7 at 22:50
oxodooxodo
32219
$endgroup$
This is regarding "using Integral Bounds to Estimate the Sum of a Series"
I do understand the proof for the integral test. However not as my book explains it.
So consider the expression below:
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangle
how does the limit s subtracted by the general expression for the reimann sum $s_{n}$ equal the sum of areas of a rectangle?
I do understand that a riemann sum for $a_{n}$ with a width of 1 gives me the area of each rectangle.
But
$s-s_{n} =sum_{k=n+1}^infty f(k)$ = sum of areas of rectangles
is lost on me.
integration convergence
integration convergence
asked Jan 7 at 22:50
oxodooxodo
32219
asked Jan 7 at 22:50
oxodooxodo
32219
asked Jan 7 at 22:50
oxodooxodo
32219
asked Jan 7 at 22:50
oxodooxodo
32219
asked Jan 7 at 22:50
oxodooxodo
32219
32219
$begingroup$
I think you'll need to write out the proof in your book, because it's impossible to follow this logic without some wider context.
$endgroup$
– Theo Bendit
Jan 7 at 23:12
add a comment |
$begingroup$
I think you'll need to write out the proof in your book, because it's impossible to follow this logic without some wider context.
$endgroup$
– Theo Bendit
Jan 7 at 23:12
$begingroup$
I think you'll need to write out the proof in your book, because it's impossible to follow this logic without some wider context.
$endgroup$
– Theo Bendit
Jan 7 at 23:12
$begingroup$
I think you'll need to write out the proof in your book, because it's impossible to follow this logic without some wider context.
$endgroup$
– Theo Bendit
Jan 7 at 23:12
add a comment |
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$begingroup$
I think you'll need to write out the proof in your book, because it's impossible to follow this logic without some wider context.
$endgroup$
– Theo Bendit
Jan 7 at 23:12