1)  1 + [ 1/ 1+2] + [ 1 / 1+ 2 + 3 ] .........n

 

2)  1/[ 1 + 1^2 +1^4 ] +  2/ [1 + 2^2 + 2^4]   + 1 / [1+ 3^2 + 3^4 ] ......n

 

3 ) 1/ [1-x][1-x^3]   + x^2/[1-x^3][1-x^5]  + x^4/[1-x^5][1-x^7]

 

4) s + a +b + c + d  prove [s-a][s-b][s-c][s-d] > 81abcd

 

5) bc , ca ,ab are in AP a> 0,b>0 ,c>0

prove a^n + c^n >2b^n