How do you evaluate the sum represented by 5n=1n2n+1 ?

1 Answer
Oct 13, 2014

First expand the series for each value of n n2n+1=12(1)+1+22(2)+1+32(3)+1+42(4)+1+52(5)+1

Next, perform the operations in the denominator...

13+25+37+49+511

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...

13 gets multiplied by 1155 giving 11553465

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

25693693=13863465,37495495=14853465,49385385=15403465and511315315=15753465

Now simply add the numerators together... 1155+1386+1485+1540+15753465

giving 71413465.