Question

write each as a summation notation

1) 2/4 +2/9 + 2/16 + 2/25 + 2/36
2) –2 + 4 – 6 + 8 – 10 + 12
3) 1 + 1/4 + 1/9 + 1/16 + 1/25
4) –3 + 6 – 9 + 12 – 15
5) 1 + 10 + 100 + 1000 + 10,000
6) 100 + 95 + 90 + 85 + 80

Answer 1

Usually it is a little daunting to have to help on multiple questions at once as a Helper :)
so just try to ask these questions one at a time next time ^_^

for these sorts of questions, try to find a pattern

like for the first one, we see that the numerator (top) is always 2
and that the denominator (bottom) seems to increase in squares
(2)^2 = 4
(3)^2 = 9
(4)^2 = 16
(5)^2 = 25
(6)^2 = 36

seeing this 2, 3, 4, 5, 6 (increasing by one) pattern means that we have found the thing to replace for "n"

so for the first question
it would kinda be like
\[\sum_{n=2}^{\infty}\frac{ 2 }{ n^2 }\]where the weird "n=2" thing means that it is increasing by 1 each time and the starts with n=2

do you get it?

Answer 2

i get that one but how do you do number 2

Answer 3

number 2 has a (-1)^n in the numerator

Answer 4

it's called an Alternating Series

Answer 5

the "n" is in the exponent for that because then if n is odd the number becomes negative
and if n is even, the number becomes positive
the 1st number was negative
then the 2nd number was positive
etc

Answer 6

the thing making the numbers in question 2
to go in the 2, 4, 6, 8, pattern
is 2(n)

so 2n * (-1)^n