What is S7 for 2+4+8+16+......? Please show steps for how you got the answer

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Answer 1 · 2018-06-03T03:27:52

#S_7 = 254#

This series sum is: #S_n = sum_(i=1)^n 2^i#

The series is a Geometric Progression (GP) with first term #a_1 = 2# and common ratio #r=2#

The sum of the first #n# terms of a GP is given by:

#S_n = (a_1(1-r^n))/(1-r)#

Therefore, in this case,

#S_7 = (2(1-2^7))/(1-2)#

#= (2(1-128))/-1#

#=254#