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1/2!+1/4!+1/6!........ upto n terms find the sum of the series

1/2!+1/4!+1/6!........ upto n terms find the sum of the series

Grade:12

1 Answers

Aditya Gupta
2081 Points
5 years ago
let S=1/2!+1/4!+1/6!........
now, we know that e^x= 1+x/1!+x^2/2!+x^3/3!+x^4/4!+.....
put x=1 and -1 successively
e= 1+1/1!+1/2!+1/3!+1/4!+...
and e^-1= 1 – 1/1!+1/2! – 1/3!+....
add the two eqns
e+1/e= 2(1+1/2!+1/4!+1/6!........)
or e+1/e= 2(1+S)
or S= [(e+1/e)/2] – 1

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