The sum to n terms of the series $$17+10+110+13+113+16+$$⋯is

Correct option is 113(7+3n−7)

Questions

The sum to $n$ terms of the series $\frac{1}{\sqrt{7} + \sqrt{10}} + \frac{1}{\sqrt{10} + \sqrt{13}} + \frac{1}{\sqrt{13} + \sqrt{16}} + \dots$ is

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13(7+3n−7)

4+3n−23

13(10+3n−10)

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detailed solution

Correct option is A

We have tr=14+3r+7+3r=7+3r−4+3r3Thus, sum to n terms is equal to13[(10−7)+(13−10)+⋯+(7+3n−4+3n)]=13(7+3n−7)

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The sum to n terms of the series 17+10+110+13+113+16+⋯is

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The sum to $n$ terms of the series $\frac{1}{\sqrt{7} + \sqrt{10}} + \frac{1}{\sqrt{10} + \sqrt{13}} + \frac{1}{\sqrt{13} + \sqrt{16}} + \dots$ is