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I need help on this question. My aunt doesn't understand it so can you help me?

1+3+3^2+3^3+3^4+••••••+3^250=?
The "^" is for Square, cube and ect.

It also includes X= 3^?-1

Can you help me please?

1 answer

note that

x^2-1 = (x-1)(x+1)
x^3-1 = (x-1)(x^2+x+1)
x^4-1 = (x-1)(x^3+x^2+x+1)

so, 3^251-1 = (3-1)(3^250+3^249+...+3^1+1)

So your sum is just (3^251-1)/(3-1)