# Search results

1. ### I Proof of series`s tail limit

Can you write Σ1∞an - ΣN+1∞an as a sum? It might be helpful to put Σ1∞an = c .
2. ### B Sum of increasing and decreasing functions

The answer may depend on what limitations you place on f, g and h in terms of continuity and differentiability. If f is continuous I can almost trivially construct functions g and h that would satisfy your criteria but be only piecewise continuous.
3. ### A Integral with an inverse function limit

Let me struggle through this in my own way. I find it useful to give familiar-looking names to things wherever possible. So let's put z-1(c) = y and ∫z(x)dx = Z, and I'll call the integral-derivative we have to evaluate F. So we have to evaluate F = (d/dc)( Z(1) -Z(y) ), which immediately...
4. ### A Logarithmic divergence of an integral

How does this sound? Your denominator is a polynomial in k; so it can be written a product of terms like (k - zi) where the zi are zeros of the polynomial. If you break this product into partial fractions, you'll automatically get a log on integration.