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

Question

freckles · Answer

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

freckles · Answer

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

freckles · Answer

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

freckles · Answer

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

freckles · Answer

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

chris215 · Answer

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

freckles · Answer

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