Aditya Gupta
Last Activity: 5 Years ago
let y = 1/n so y tends to 0+
so L= lim y tends to 0+ { (1+y)m + ( 1 + 2y)m + …..+ (1+ky)m – k}/y
now write – k= – 1 – 1 …...... – 1 (k times)
L= lim y tends to 0+ [{(1+y)m – 1} + {( 1 + 2y)m – 1}+ …..+ {(1+ky)m – 1}]/y
= lim y tends to 0+ {(1+y)m – 1}/y + lim y tends to 0+ {(1+2y)m – 1}/y + …...... + lim y tends to 0+ {(1+ky)m – 1}/y
now, note that lim y tends to 0+ {(1+py)m – 1}/y= mp (by l hopital)
so, L = 1*m + 2*m + …..... + k*m
= mk(k+1)/2
kindly approve :)
