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Grade 12Algebra

Sobe the question given in attached image......................................?............

Question image for Sobe the question given in attached image........

Sarvesh

7 Years agoGrade 12

1 Answer

Omkar Doiphode

7 Years ago

S_n+1-S_n= (a₁+a₂+....+a_n+a_n+1) - (a₁+a₂+....+a_n) = a_n+1

Now,

$\lim_{n\rightarrow \infty} a_{n+1} = \lim_{n\rightarrow \infty} a_{n} = 2$

also,

$\sum_{k=1}^{n} = \frac{n(n+1)}{2}$

Now Lets try to simplify the equation

$\lim_{n\rightarrow \infty } \frac{Sn+1-Sn}{\sum_{k=1}^{n}k} = \lim_{n\rightarrow \infty } \frac{a_{n+1}}{\frac{n(n+1))}{2}} = \frac{ \lim_{n\rightarrow \infty }a_{n+1}}{ \lim_{n\rightarrow \infty }\frac{n(n+1))}{2}} =\tfrac{4}{{ \lim_{n\rightarrow \infty }\frac{n(n+1))}{1}}} = 0$

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