Question

Find the value of \[ 1 + {1\cdot2\over1\cdot3} + {1\cdot2\cdot3\over1\cdot3\cdot5}+ {1\cdot2\cdot3\cdot4\over 1\cdot3\cdot5\cdot7} +\cdots \]

Answer 1

*

Answer 2

its like,

n/n + (n)(n+1)/n(n+2) + (n)(n+1)(n+2)/n(n+2)(n+4) ... so a series

numerator = n (n+1)/2.. addition of consecutive integers
and denominator = n(n+1)... addition of all consecutive even integers

so = n(n+1)/ 2(n)(n+1)

So = 1/2...

Not sure, just a try...

Answer 3

\[ 1 + {\pi \over 2}\]