Question

ex: 28 - C,D. Aratati ca

Answer 1

Răspuns:

Explicație pas cu pas:

3=M₄+3 (multiplu de 4+...)

3²=M₄+1

3³=M₄+3

3⁴=M₄+1

................

3²⁰⁰³=M₄+3

3²⁰⁰⁴=M₄+1

C=(M₄+3)+(M₄+1)+...+(M₄+3)+(M₄+1)=M₄

Sau altfel:

C = 3*(1+3)+3³*(1+3)+...3²⁰⁰³*(1+3)= 4* (3¹+3³+...+3²⁰⁰³) = M₄

D = (7¹+7²+7³)+(7⁴+7⁵+7⁶)+...+(7²⁰⁰²+7²⁰⁰³+7²⁰⁰⁴)=

= 7*(1+7+7²)+7⁴(1+7+7²)+...+7²⁰⁰²(1+7+7²) = (1+7+7²)*(7+7⁴+...+7²⁰⁰²) =

= 57* (7+7⁴+...+7²⁰⁰²) = M₅₇