# Real analysis

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

https://brainmass.com/math/real-analysis/real-analysis-summation-26504

#### 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 ...

#### Solution Summary

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

$2.19