Question

Express the sum using sigma notation: 1/2+2/5+3/10+4/17+5/26

Answer 1

top is going up be 1 each time
the bottom is a quadratic because the second differences are constant

that is 2,5,10,17,26
first differences 3,5,7,9
second difference: 2,2,2

Answer 2

find a,b,c given
\[f(n)=an^2+bn+c \text{ and } \\ f(1)=2 \\ f(2)=5 \\ f(3)=10 \\ ,...\]

Answer 3

using just that you will have a system of equations with 3 equations and 3 variables

Answer 4

you can solve that to find a,b, and c

Answer 5

however if you want to try to short cut things you can try to guess the quadratic pattern in the denominator

Answer 6

i got the summation from k = 1 to 5 k+1/(k^2)

Answer 7

here is a hint for the denominator: 2=1^2+1, 5=2^2+1,10=3^2+1,.....
also it looks your numerator needs a little fixing