Question

Solve: 1/1 + 1/1+2 + 1/1+2+3+.. .... ..+1/1+2+3+.... ...+12​

Answer 1

Answer:

$\frac{1}{1} + \frac{1}{1 +2} + \frac{1}{1 + 2 + 3} + .. \: .. + \frac{1}{1 + 2 + .. + 12}$

Sn = T1+T2+T3.. +Tn

Tn =

$\frac{1}{1 + 2 +.. n}$

$= \frac{1}{ \frac{n \times n + 1}{2} } + \frac{2}{n \times n + 1} = 2 \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + .. \: .. \: .. + \frac{1}{n(n + 1)} \\ = 2( \frac{1}{1} - \frac{1}{2} + \frac{1}{2}.. \: .. + \frac{1}{n} - \frac{1}{n + 1} \\ same \: terms \: will \: be \: cutted.. \\ = 2( \frac{1}{1} - \frac{1}{n + 1}) \\ = 2 (\frac{1}{1} - \frac{1}{12 + 1} ) \\ = 2( \frac{1}{1} - \frac{1}{13}) \\ = 2( \frac{13 - 1}{13} ) \\ = 2 \times \frac{12}{13} \\ = \frac{24}{13}$

Step-by-step explanation:

Hope this helps You

Happy Learning

Answer 2

Step-by-step explanation:

hi sis I m radha sis

I think u had forgotten me or what

I missing u lot sis..

radhe radhe

jai shri Krishna