Question

C= 3⁰-3¹+3²-3³+........+3⁶²-3⁶³

 

Answer 1

C=\(\frac{1-3^{64}}{4}\)

Answer 2

=> 3C = 3 - 3² + 3³ - 3⁴ + .............. + 3⁶³ - 3⁶⁴

=> 3C + C = (3 - 3² + 3³ - 3⁴ + .............. + 3⁶³ - 3⁶⁴) + (1 - 3 + 3² - 3³ + .......... + 3⁶² - 3⁶³)

=> 4C = 1 - 3⁶⁴

=> C = \(\frac{1-3^{64}}{4}\)

Answer 3

=> \(3C=3^1-3^2+3^3-3^4+...+3^{63}-3^{64}\)

=> \(3C+C=\left(3^1-3^2+3^3-3^4+...+3^{63}-3^{64}\right)+\left(3^0-3^1+3^2-3^3+...+3^{62}-3^{63}\right)\)

=> \(4C=\left(-3\right)^{64}+3^0\)

=> \(C=\frac{\left(-3\right)^{64}+1}{4}\)