Question

Got a horrible question from Calculus whoever can solve it
Evaluated

Limit n →infty 1/n[(1/n)^7+(2/n)^7+(3/n)^7+...+(n/n)^7]

Answer 1

here is a hint:
corresponding of mean value theorem f'=g' → f=g+c

\[\int\limits_{1}^{xy}(1/t) dt=\int\limits_{1}^{x} (1/t) dt + \int\limits_{1}^{y} (1/t) dt +c\]

x=1

\[\int\limits_{1}^{y}(1/t)dt=\int\limits_{1}^{1}(1/t) dt+ \int\limits_{1}^{y} (1/t) dt+c\]
0=c

Answer 2

f(x): continue on [a,b]