Chapter 14, Problem 171P

Which of the following sequences converge and which diverge? 1) a₁ = 2+(0.1)" 1-2n 2) a = 1+2n 1/n 3 16) a = n In n 17) an = n 1/n 1-5n4 3) an = n² +8n³ 18) an = √4" n n² -2n+1 n! 20) a = 4) an = 106 5) n-1 a₁ =1+(-1)" n+1 a-(+) (1-4) 6) = 7) a = 2n (-1)"+1 2n-1 21) an = n -A" 1/(Inn) 3n+1 22) a = 3n-1 1/n x" 23) a = , x>0 2n+1 3" x 6" 24) a = 2™" xn! 2n 8) a = n+1 πT 1 9) a„ = sin +- 2 n sin n 10) an = n 25) a = tanh(n) 26) a = 2n-1 27) a = tan(n) 1 -sin n n 11) a = 2" 28) an == " 1 + 2" In(n+1) 12) a = n (In n) 200 29) a = n 13) a = 8/n 14) a 1+ =(1+²)" 15) an 7 n = 10n 30) an-√√n²-n 1"1 31) adx nix

A steel alloy contains 95.7 wt% Fe, 4.0 wt% W, and 0.3 wt% C.

b. A horizontal cantilever of effective length 3a, carries two concentrated loads W at a distance a from the fixed end and W' at a distance a from the free end. Obtain a formula for the maximum deflection due to this loading using Mohr's method. If the cantilever is 250 mm by 150mm steel I beam, 3 m long having a second moment of area I as 8500 cm4, determine W and W'to give a maximum deflection of 6 mm when the maximum stress due to bending is 90 Mpa. Take Young's modulus of material E as 185 Gpa.