let m and k be positive integers (m not equal to

Question

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:

Aditya Gupta · Accepted 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}/ynow 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}/ynow, 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)/2kindly approve :)

Integral Calculus> let m and k be positive integers (m not e...

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:

Meghana , 6 Years ago

Aditya Gupta

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Integral Calculus> let m and k be positive integers (m not e...

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:

Meghana , 6 Years ago

Aditya Gupta

LIVE ONLINE CLASSES

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