The sum of the serier $${1 \over {1.2}} - {1 \over {2.3}} + {1 \over {3.4}}..............$$ up to $$\infty $$ is equal to

$${1^3} - \,\,{2^3} + {3^3} - {4^3} + ... + {9^3} = $$

l, m, n are the $${p^{th}}$$, $${q^{th}}$$ and $${r^{th}}$$ term of a G.P all positive, $$then\,\left| {\matrix{ {\log \,l} & p & 1 \cr {\log \,m} & q & 1 \cr {\log \,n} & r & 1 \cr } } \right|\,equals$$

Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is