S₅ =b₁(1-q^5)/(1-q) . * * * { b₁q³ =1/16 ;{ b₁q^4 =1/64 . * * *
q =b₅/b₄ =(1/64) / (1/16) =1/4.
b₁*q³ =1/16 ;
b₁*(1/4)³ =1/16⇒b₁ = 4 .
S₅ =b₁(1-q^5)/(1-q) = 4(1 -(1/4)^5)/ (1 -1/4)=4² (1 -1/4^5)/3 = 16(1 - 1/1024)/3=1023/3*64=
= 341/64.
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проверка: 4+1+1/4+1/16+1/64 =(256+64 +16+4+1)/64 =341/64.