Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation.
-$$5 ^ { 2 } + 10 ^ { 3 } + 15 ^ { 4 } + \ldots + 40 ^ { 9 }$$
A) $\sum _ { \mathrm { i } = 1 } ^ { 8 } ( 5 \mathrm { i } ) ^ { \mathrm { i } + 1 }$
B) $\sum _ { i = 1 } ^ { 8 } ( 5 i ) ^ { i }$
C) $\sum _ { i = 1 } ^ { 8 } 2 ( i - 1 ) ^ { i + 1 }$
D) $\sum _ { i = 1 } ^ { 8 } 5 i ^ { 2 i - 1 }$

Question

Quizplus · Accepted Answer

The given series can be expressed in the form $(5i)^{i+1}$ where $i$ starts from 1 and goes up to 8, because the base increases by 5 each time (5, 10, 15, ..., 40) and the exponent starts at 2 and increases by 1 each time (2, 3, 4, ..., 9), which matches the pattern of $i+1$ for the exponent when $i$ starts from 1.

Express the Sum Using Summation Notation 52+103+154+…+4095 ^ { 2 } + 10 ^ { 3 } + 15 ^ { 4 } + \ldots + 40 ^ { 9 }52+103+154+…+409

Express the Sum Using Summation Notation $5 ^ { 2 } + 10 ^ { 3 } + 15 ^ { 4 } + \ldots + 40 ^ { 9 }$