Question 1 Review Exercise 5

i. If $t_n=6 n+5$ then $t_{n+1}=$

• (a) $6 n-1$
• (b) $6 n+11$
• (c) $6 n+6$
• (d) $6 n-5$
  See Answer

  (b): $6 n+11$

ii. The sum to infinity of the series: $1+\dfrac{2}{3}+\dfrac{6}{3^2}+\dfrac{10}{3^3}+\dfrac{14}{3^4}+\ldots$

• (a) $6$
• (b) $2$
• (c) $3$
• (d) $4$
  See Answer

  ©: $3$

iii. Sum the series:$1+2.2+3.2^2+\cdots+100.2^{\prime \prime}$

• (a) $99.2^{100}$
• (b) $100.2^{100}$
• (c) $99.2^{100}+1$
• (d) $1000.2^{100}$
  See Answer

  ©: $99.2^{100}+1$

iv. The $n^{t h}$ term of the series: $1.2+2.3+3.4+\ldots$

• (a) $n^2-n$
• (b) $n^2+n$
• (c) $n^2$
• (d) None of these
  See Answer

  (b): $n^2+n$

v. Sum of $n$ terms of the series whose $n^{t h}$ term is $1+2^n$

• (a) $n \cdot 2^{n-1}$
• (b) $(n+1)+2^{n+1}$
• (c) $n+2(2^n-1)$
• (d) None of these
  See Answer

  ©: $n+2(2^n-1)$

vi. Evaluate $\Sigma\left(3+2^r\right)$, where $r=1,2,3, \ldots, 10$

• (a) $2051$
• (b) $2049$
• (c) $2076$
• (d) $1052$
  See Answer

  ©: $2076$

vii. What is the $n$ term of the series: $1+\dfrac{1+2}{2}+\dfrac{1+2+3}{3}+\ldots$

• (a) $\dfrac{n+1}{2}$
• (b) $\dfrac{n(n+1)}{2}$
• (c) $n^2-(n+1)$
• (d) $\dfrac{(n+1)(2 n+3)}{2}$
  See Answer

  (a): $\dfrac{n+1}{2}$

viii. Sum of $n$ terms of the series $1^3+3^3+5^3+7^3+\ldots$

• (a) $n^2(2 n^2-1)$
• (b) $2 n^3+3 n^2$
• (c) $n^3(n-1)$
• (d) $n^3+8 n+4$
  See Answer

  (a): $n^2(2 n^2-1)$