Find the sum of 1-2 - 1-2-3 - 1-3-4 - - - - - - 1-10-11-

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Subtraction of Integers

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Question

Find the sum of 1\12 + 1/23 + 1/34 + _ _ _ _ + 1/1011.

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Solution

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1 + \frac{2}{11} + \frac{5}{11^{2}} + \frac{10}{11^{3}} + \frac{17}{11^{4}} + . .

{c o t}^{- 1} (1 + \frac{3}{4}) + {c o t}^{- 1} (2^{2} + \frac{3}{4}) + {c o t}^{- 1} (3^{2} + \frac{3}{4}) + . . . . . \infty

{s i n}^{- 1} (\frac{1}{\sqrt{2}}) + {s i n}^{- 1} (\frac{\sqrt{2} - 1}{\sqrt{6}}) + . . . + {s i n}^{- 1} [\frac{\sqrt{n} - \sqrt{n - 1}}{\sqrt {n (n + 1)}}] + . . . . \infty

\frac{2}{⌊ 1} + \frac{3}{⌊ 2} + \frac{6}{⌊ 3} + \frac{11}{⌊ 4} + \frac{18}{⌊ 5} + . . . .

\frac{- 3}{11}, \frac{- 1}{4} a n d \frac{5}{8}

\frac{3}{1 \cdot 2} (\frac{1}{2}) + \frac{4}{2 \cdot 3} {(\frac{1}{2})}^{2} + \frac{5}{3 \cdot 4} {(\frac{1}{2})}^{3} + \dots

n

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