SPECIAL APPLICATIONS OF ANALYSIS 151 



7.175 



2. [(7r - 2#)tan ^]TT = 2. 6. 



[,.'/ #\ , 7TX~\ 2 



S^-J-~nJ~T ?- 



^ >. 8. [<tan * 



2 



7.18 Limiting Values of Sums. 



Limit/i^ + 2 k + 3* + . . . . + n k \ i 

 n > oo \ n k+l / k + i 



oo if k<, i. 



Limit /iii i 



2.. ( + r+ i +....+ 



\wa na + b na + 2b na + (n - i 



log (g + b) - log g 



Limit / n i 2 n 2 2 ^ 3 2 



3 * -2-(+ i) + 2-3- 0+ 2) + 3-4'( + 



(w - w 2 



1 a 2 

 if a is a positive proper fraction. 



if b>o and a is a positive proper fraction. 

 6 . L 



i-V^ 

 if 6>o and a is a positive proper fraction. 



(6.602). 



