Do you need an exact fraction, or will a decimal approximation do?
For a decimal approximation, on an algebraic calculator just enter what you did above. For a standard calculator that has a [1/x] key, enter:
94 [1/x] + 95 [1/x] + 96 [1/x] + 97 [1/x] + 98 [1/x] + 99 [1/x] + 100 [1/x] =
With no [1/x[ key, but order of operations are honored (most of the rest):
1 ÷ 94 + 1 ÷ 95 + 1 ÷ 96 + 1 ÷ 97 + 1 ÷ 98 + 1 ÷ 99 + 1 ÷ 100 =
If you need an exact fraction, it' helps to find the least common multiple, and that's a 12 digit number. Call it d, and it's equal to:
d = 336158776800
If you multiply that sum by (1/d)*d you get, (1/d)(d/94 + d/95 + d/96 + ... + d/100). Every term in the sum here is a whole number, since d is divisible by each of the numbers from 94 to 100. That gets you the fraction:
24269201533 / 336158776800
Trust me, it's in least terms. If your calculator doesn't let you input 10 digit numbers, you won't be able to get this result exactly. What you do get probably won't be better than what you'd get from the approximations above, an they're easier.