A P Prabhakaran Solutions for Chapter: Sequence and Series, Exercise 2: SELF EVALUATION TEST

Find the sum of the series $0.3+0.33+0.333+\dots$to $n$ terms

Find the sum of all integers between $50$ and $450$ which are divisible by $7$.

If $p^{th}$ term of an $A.P$ is $q$ and $q^{th}$ term is $p$ show that $r^{th}$ term is $p+q-r$

If the first term of an $A.P$ is $2$ and the sum of first $5$ terms is equal to one-fourth of sum of next five terms, find the sum of first $30$ terms.

If the $m^{th}$ term of an $A.P$ is $\frac{1}{n}$and the $n^{th}$ term is $\frac{1}{m}$, show that the sum first $mn$ terms is $\frac{1}{2}(mn+1)$

Find three numbers in$A.P$ whose sum is $12$ and the sum of the squares is $66$.

Find the sum of the series $2^2+4^2+6^2+\cdots +(2n{)}^2$

In an increasing $\mathrm{G}.\mathrm{P}$, the sum of first and last term is $66$, the product of second and the last but one term is $128$. If the sum of the series $126$, find the number of terms of the series?