Purchase Solution

Real analysis

Not what you're looking for?

Ask Custom Question

Show that if sum(sum sign) to infinity(top) of k=1(bottom) of a_k=A and sum(sum sign) to infinity(top) of k=1(bottom) of b_k=B, then
1-sum(sum sign) to infinity(top) of k=1(bottom) of ca_k=cA for all c belong to R
2-sum(sum sign) to infinity(top) of k=1(bottom) of (a_k+b_k)=A+B

Purchase this Solution

Solution Summary

There are several proofs regarding summations in this solution. The infinite loop function is given.

Solution Preview

1)
We know that the series converges to A. That means
lim s_k= lim (a_1 + a_2 + ... + a_k) = A
k--->infinity

Now we know from the standard laws of lim that if:

lim (f(x))= L
x--->h
then ...

Purchase this Solution


Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts