Question

Помогите пожалуйста!

Нужно найти n

Answer 1

Ответ: n = 481.

Пошаговое объяснение:

$dfrac{1}{a_1a_2}+dfrac{1}{a_2a_3}+dots+dfrac{1}{a_{n-1}a_n}=-dfrac{1}{d}left(dfrac{1}{a_1(a_1+d)}+dfrac{1}{(a_1+d)(a_1+2d)}+dots +$

$dfrac{1}{(a_1+(n-2)d)(a_1+(n-1)d)}bigg)=-dfrac{1}{d}left(dfrac{a_1-(a_1+d)}{a_1(a_1+d)}+dfrac{a_1+d-(a_2+2d)}{(a_1+d)(a_1+2d)}+$

$+dots +dfrac{a_1+(n-2)d-(a_1+(n-1)d)}{(a_1+(n-2)d)(a_1+(n-1)d)}bigg)=-dfrac{1}{d}bigg(dfrac{1}{a_1+d}-dfrac{1}{a_1}+dfrac{1}{a_1+2d}-\ \ -dfrac{1}{a_1+d}+...+dfrac{1}{a_1+(n-1)d}-dfrac{1}{a_1+(n-2)d}bigg)=dfrac{1}{d}bigg(dfrac{1}{a_1}-dfrac{1}{a_n}bigg)=20\ \ d=dfrac{1}{20}times bigg(dfrac{1}{12}-dfrac{1}{2}bigg)\ \ d=-dfrac{1}{48}\ \ a_n=a_1+(n-1)d~~Leftrightarrow~~ n=481$