Hello.
How to prove that those operations are truth?
Sums

a. This is just shifting the index of summation:

and just swap j with k, since you can freely use any symbol for the index.

That is, the identity relies on simple integer arithmetic: 0 + 1 = 1 = 2 - 1, and 1 + 1 = 2 = 3 - 1, and so on.

b. This is something of a generalization of the identity in part a.

c. Distribute the summation to get

The second sum here is just adding together m copies of 1,

so

d. The sum as given is generally not true:

while (generalizing the identity from part c)

and these expressions are equal only if .

1

step-by-step explanation:

you are throwing one dart

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer