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5+5²+5³+5⁴+....+5¹⁰⁰¹
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Sagot :

Discipulusidn

Answer:

[tex]S_n = \frac{[a_1(1-q^n)]}{(1-q)} \\ S_{1001} = = \frac{5(1 - {5}^{1001}) }{1 - 5} [/tex]

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If we write the above numbers separately, we will see that we have a geometric sequence with the first term 5 ( t(1) = 5 ) and the ratio of 5 ( q = 5 ) :

5 ، 25 ، 125 ، 625 ، ...

The sum of the first n terms ( S (n) ) of a geometric sequence is obtained from the following equation :

S ( n ) = t(1) × ( q^n - 1 / q - 1 )

S ( 1001 ) = 5 × ( 5^1001 - 1 / 5 - 1 )

S ( 1001 ) = 5 × ( 5^1001 - 1 / 4 )

S ( 1001 ) = 5/4 × ( 5^1001 - 1 )

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