let m and k be positive integers (m not equal to k) Then lim n --- infinty n { (1+1/n) m + ( 1 + 2/n) m + …..+ (1+k/n) m – k} is:

Question

let m and k be positive integers (m not equal to k) Then lim n ---> infinty n { (1+1/n) m + ( 1 + 2/n) m + …..+ (1+k/n) m – k} is:

Aditya Gupta · Answer

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 :)

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let m and k be positive integers (m not equal to k) Then lim n ---> infinty n { (1+1/n) m + ( 1 + 2/n) m + …..+ (1+k/n) m – k} is:

let m and k be positive integers (m not equal to k)
Then
lim_{n ---> infinty}n { (1+1/n)^m+ ( 1 + 2/n)^m + …..+ (1+k/n)^m – k} is:

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let m and k be positive integers (m not equal to k) Then lim n ---> infinty n { (1+1/n) m + ( 1 + 2/n) m + …..+ (1+k/n) m – k} is:

let m and k be positive integers (m not equal to k)Thenlimn ---> infinty n { (1+1/n)m + ( 1 + 2/n)m + …..+ (1+k/n)m – k} is:

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let m and k be positive integers (m not equal to k)
Then
lim_{n ---> infinty}n { (1+1/n)^m+ ( 1 + 2/n)^m + …..+ (1+k/n)^m – k} is: