Question
Download Solution PDF\(\rm \frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} +...+\frac{1}{{n \times (n+1)}} \) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFगणना:
\(\rm \frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} +...+\frac{1}{{n \times (n+1)}} \)
\(\rm = \frac{{2\; - \;1}}{{1 \times 2}} + \frac{{3\; - \;2}}{{2 \times 3}} + \frac{{4\; - \;3}}{{3 \times 4}} +... + \frac{{(n+1)\; - \;n}}{{n \times (n+1)}}\)
\(\rm = \frac{1}{1} - \frac{1}{2} + \;\frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} +... + \frac{1}{n} - \frac{1}{n+1}\)
\(\rm = 1 - \frac {1}{n+1}\)
\(\rm = \frac {n+1 -1}{n+1}\)
\(\rm = \frac {n}{n+1}\)
Last updated on May 19, 2025
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