How do you use summation notation to expression the sum #7+14+28+...+896#?

1 Answer
Feb 16, 2017

Answer:

# sum_(r=0)^(127) \ 7 + 7r \ \ # or # \ \ sum_(r=1)^(128) 7r#

Explanation:

Let #S = 7+14+28+ ... + 896 #

The first term is #7#, and we get subsequent terms by adding #7# each time, so the series is:

# S= 7 + (7+7) + (7+2(7)) + (7+3(7)) + ... 896 #
# \ \ = 7 + (7+7) + (7+2(7)) + (7+3(7)) + ... (7+(127)7) #
# \ \ = sum_(r=0)^(127) \ 7 + 7r#

Alternatively if you prefer the sum to start from #r=1# we could write:

# S= (0+(1)7) + (0+(2)7) + (0+3(7)) + (0+(128)7) #
# \ \ = sum_(r=1)^(128) 7r#

(NB the sum evaluates to #S=57792#)