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

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Answer 1 · 2014-10-13T21:32:46

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 $7141/3465$ .

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