Series

Question 1

Prove sum of integers of arithemetic series

Answer 1

1. Sn = a + (a+d) + (a+2d) … (a+(n-2)d) + (a+(n-1)d)
2. Sn = (a+(n-1)d) + (a+(n-2)d) … (a+2d) + (a+d) + a
3. add formulas together
4. Sn + Sn = (2a+(n-1)d) + (2a + (n-1)d) …. (2a(n-1)d)
5. 2Sn = n(2a+ (n-1)d)
6. Sn = n/2(2a+(n-1)d)

Question 2

Un arithemtic

Answer 2

a + (n-1)d

Question 3

Sn arithmetic

Answer 3

n/2(2a + (n-1)d)

Question 4

Sum to infifinity

Answer 4

a / 1-r

Question 5

Un geometric

Answer 5

ar^(n-1)

Question 6

Sn geometric

Answer 6

a(1-r^n)/1-r

or a(r^n-1)/r-1