111+n + 11Problem 7. Let cn =Σ+2nn + k°k=0(a) Calculate c1, c2, C3, and c4.2n2n11dx +11dx +2n(b) Show that< Cn <(Hint: Begin by approximating this integral using twon.-1= xdifferent Riemann sums of f(x)the other using right endpoints.)over [n, 2n] with Ax1, one Riemann sum using left endpoints, and%3D(c) Find lim Cn using the squeeze theorem.n→∞

(a) Given: cn=1n+1n+1+⋯+12n=∑k=0n1n+k So, c1=1c2=1+12=32c3=1+12+13=116c4=1+12+13+14=2512

Problem 7. Let cn = +...+ 2n Σ. n + 1 n + k k=0 n (a) Calculate c1, C2, C3, and c4. c2n 2n 1 - dx + 1 < Cn < 1 - dx + 1 (b) Show that (Hint: Begin by approximating this integral using two 2n different Riemann sums of f(x) = x¯ over [n, 2n] with Ax = 1, one Riemann sum using left endpoints, and the other using right endpoints.) (c) Find lim cn using the squeeze theorem.