De Anza College Sequences Converge or Diverge Question

Question Description

) Determine whether the following sequences converge or diverge. If they converge, indicate what theyconverge to. If they diverge to ? or to ??, say so.(a) an =?9n3+17n?n+1(b) an = sin6n2 ?49n4 ? 9n2 + 16(c) an =sin nn(be sure to fully justify your answer)(d) an =1 ?2n n(be sure to fully justify your answer)(2) Suppose that ai ? ai+1 for all i ? 100, and that ai ? 17 for all i ? 100. Can we conclude whetherthe sequence (ai)?i=1 converges or not? Why or why not? If we can conclude it converges, what canwe conclude about the limit?(3) Find the values of the following geometric sums.(a) Pni=02i5(b) Pni=1 8?23 i(4) Find the value of Pni=112n (This one is tricky; notice that is 2n in the summation, not 2i)(5) Determine whether the following series converge or diverge. Justify your answers. If a series converges, state what it converges to.(a) P?i=3813i(b) P?i=1i+42i+6(c) P?i=1(?1)i5(6) Suppose that limi?? ai = 0. Can we conclude that P?i=1 ai conv

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