How do you evaluate the sum represented by sum_(n=1)^5n/(2n+1) ?

1 Answer
Oct 13, 2014

First expand the series for each value of n n/(2n+1)=1/(2(1)+1+2/(2(2)+1+3/(2(3)+1+4/(2(4)+1+5/(2(5)+1

Next, perform the operations in the denominator...

1/(3)+2/5+3/7+4/9+5/11

Now, to add fractions we need a common denominator... in this case it's 3465

Next, we have to multiply each numerator and denominator by the missing components...

1/3 gets multiplied by 1155 giving 1155/3465

(Divide the 3465 by 3 to get 1155 and divide the rest by the given denominator.)

2/5*693/693=1386/3465, 3/7*495/495=1485/3465, 4/9*385/385=1540/3465 and 5/11*315/315=1575/3465

Now simply add the numerators together... (1155+1386+1485+1540+1575)/3465

giving 7141/3465.