11 11+2 + 12+3+13+4+14+5+15+6+16+7+17+8+18+9Now, 11+2 = 11+2×1-21-2 = 1 - 21 - 2 = 2 - 1Now, 12+3 = 12+3×2-32-3 = 2 - 32 - 3 = 3 - 2Similarly, we get13+4 = 4-314+5 = 5-415+6 = 6-516+7 = 7 - 617+8 = 8 - 718+9 = 9-8Now, 11+2 + 12+3+13+4+14+5+15+6+16+7+17+8+18+9=2-1+3-2+4-3+5-4+6-5+7-6+8-7+9-8=-1+9=-1+3=2 Kindly ask the remaining queries in different threads

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(11) . \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} Now, \frac{1}{1 + \sqrt{2}} = \frac{1}{1 + \sqrt{2}} \times \frac{1 - \sqrt{2}}{1 - \sqrt{2}} = \frac{1 - \sqrt{2}}{1 - 2} = \sqrt{2} - 1 Now, \frac{1}{\sqrt{2} + \sqrt{3}} = \frac{1}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}} = \frac{\sqrt{2} - \sqrt{3}}{2 - 3} = \sqrt{3} - \sqrt{2} Similarly, we get \frac{1}{\sqrt{3} + \sqrt{4}} = \sqrt{4} - \sqrt{3} \frac{1}{\sqrt{4} + \sqrt{5}} = \sqrt{5} - \sqrt{4} \frac{1}{\sqrt{5} + \sqrt{6}} = \sqrt{6} - \sqrt{5} \frac{1}{\sqrt{6} + \sqrt{7}} = \sqrt{7} - \sqrt{6} \frac{1}{\sqrt{7} + \sqrt{8}} = \sqrt{8} - \sqrt{7} \frac{1}{\sqrt{8} + \sqrt{9}} = \sqrt{9} - \sqrt{8} Now, \frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = \sqrt{2} - 1 + \sqrt{3} - \sqrt{2} + \sqrt{4} - \sqrt{3} + \sqrt{5} - \sqrt{4} + \sqrt{6} - \sqrt{5} + \sqrt{7} - \sqrt{6} + \sqrt{8} - \sqrt{7} + \sqrt{9} - \sqrt{8} = - 1 + \sqrt{9} = - 1 + 3 = 2

Kindly ask the remaining queries in different threads.

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