To add these fractions together, we need a common denominator for each pair of radicals.
For the first pair, we can multiply the numerator and denominator of the first fraction by √2 to get a common denominator:√1√2/√2√2 + √2/√2√2
This gives us:(√2 + 2)/2√2
Similarly, for the second pair:√2√3/√3√3 + √3/√3√3(√6 + 3)/3√3
Continuing this pattern, the sum of all the given fractions would be:(√2 + 2)/2√2 + (√6 + 3)/3√3 + ... + (√2016 + 45)/45√2017
This can be simplified by finding a common denominator for all terms and adding the numerators together.
To add these fractions together, we need a common denominator for each pair of radicals.
For the first pair, we can multiply the numerator and denominator of the first fraction by √2 to get a common denominator:
√1√2/√2√2 + √2/√2√2
This gives us:
(√2 + 2)/2√2
Similarly, for the second pair:
√2√3/√3√3 + √3/√3√3
(√6 + 3)/3√3
Continuing this pattern, the sum of all the given fractions would be:
(√2 + 2)/2√2 + (√6 + 3)/3√3 + ... + (√2016 + 45)/45√2017
This can be simplified by finding a common denominator for all terms and adding the numerators together.