



 
Hi Rahul, Let's try this with $n = 3.$ The sum is then \[ \sum_{k=1}^{k=3} x^k\] which unpacks to \[x^1 + x^2 + x^{3}.\] Thus you have \[\int_{0}^{b} {1 + x^1 + x^2 + x^3} dx.\] Evaluate this definite integral and rewrite the answer using summation notation. Can you make it look like the answer given in your question with $n = 3?$ This works because the integral of a sum is the sum of integrals. That is \[\int_{0}^{b} {1 + x^1 + x^2 + x^3} dx = \int_{0}^{b}{1}\; dx+ \sum_{k=1}^{k=3} {\int_{0}^{b} {x^k}}{dx}. \] Try to repeat this with $k = 1$ to $k = n.$ Write back if you need more assistance,  


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