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Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 1+1/2+(1/2)^2+(1/2)^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.|+(1/2)^98+(1/2)^99+(1/2)^100 .
Question type: Mathematical calculation
Solution:
1+1/2+(1/2)^2+(1/2)^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.|+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+(1/2)^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+(1/2)^7+(1/2)^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+(1/2)^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+(1/2)^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0.+(1/2)^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0.+0.5^98+(1/2)^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0.+0.5^98+0.5^99+(1/2)^100
=1+1/2+0.5^2+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0.+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.5^3+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.5^4+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.5^5+0.5^6+0.5^7+0.5^8+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.5^6+0.5^7+0.5^8+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.5^7+0.5^8+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.5^8+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.5^9+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0.5^98+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0.5^99+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0.5^100
=1+1/2+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1+0.5+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.5+0.25+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.75+0.125+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.875+0.0625+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.9375+0.03125+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.96875+0.015625+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.984375+0.0078125+0.00390625+0.001953125+0+0+0+0
=1.992188+0.00390625+0.001953125+0+0+0+0
=1.996094+0.001953125+0+0+0+0
=1.998047+0+0+0+0
=1.998047+0+0+0
=1.998047+0+0
=1.998047+0
=1.998047
Answer:1+1/2+(1/2)^2+(1/2)^3+(1/2)^4+(1/2)^5+(1/2)^6+(1/2)^7+(1/2)^8+(1/2)^9+0.|+(1/2)^98+(1/2)^99+(1/2)^100=1.998047