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Viluxent Set 1 Paper 2 · Q8

Paper 2Sequences & series

Find the value of

∑k=116801kk+1+(k+1)k.\sum_{k=1}^{1680}\frac{1}{k\sqrt{k+1}+(k+1)\sqrt{k}}.
A141\frac1{41}
B3941\frac{39}{41}
C4041\frac{40}{41}
D4142\frac{41}{42}
E11
F16801681\frac{1680}{1681}

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