Express the sum using summation notation. Use a lower limit of summation, not necessarily 1, and k for the index of
summation.
-$$( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$$
A) $\sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } \left( \mathrm { a } + \mathrm { b } ^ { \mathrm { k } } \right)$
B) $\sum _ { \mathrm { k } = 0 } ^ { \mathrm { n } } a \mathrm {~b} ^ { \mathrm { k } }$
C) $\sum _ { k = 0 } ^ { n } \left( a + b ^ { k } \right)$
D) $\sum _ { k = 0 } ^ { n - 1 } \left( a + b ^ { k } \right)$

Question

Quizplus · Accepted Answer

The given series starts with $a + 1$ which corresponds to $b^0$ (since $b^0 = 1$ for any $b$), and ends with $a + b^n$. This matches option C, where the summation starts from $k = 0$ to $n$, correctly representing the series from $a + b^0$ to $a + b^n$.

Express the Sum Using Summation Notation (a+1)+(a+b)+(a+b2)+…+(a+bn)( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)(a+1)+(a+b)+(a+b2)+…+(a+bn)

Express the Sum Using Summation Notation $( a + 1 ) + ( a + b ) + \left( a + b ^ { 2 } \right) + \ldots + \left( a + b ^ { n } \right)$