Find the sum `(3)/(2) - (5)/(6) + (7)/(18) -(9)/(54)+ cdotsoo`

Find the sum ""^(10)C_(1) +^(10)C_(3) +^(10)C_(5)+^(10)C_(7)+^(10)C_(9) .

Consider the points A (3,2,-4), B (5,4,-6) and C (9,8,-10) Using section formula, prove that A, B, C are collinear.

Find the sum of n terms of the series 1 + 4/5 + 7//5^(2) + 10//5^(3)+ cdots

The sum S= 1/(9!)+1/(3!7!)+1/(5!5!)+1/(7!3!)+1/(9!) is equal to

Given that P (3,2,-4), Q(5,4,-6) and R(9,8,-10) are collinear. Find the ratio in which Q divides PR.

Consider the points A(3,2,-4),B(5,4,-6) and C(9,8,-10).(i)Find AB,BC and AC and show that A,B,C are collinear.

Consider the points A(3,2,-4),B(5,4,-6) and C(9,8,-10).(ii)Find the ratio in which B divides AC using distance formula.

Given that P(3,2,-4), Q(5,4,-6) and R(9,8,-10) are collinear. Find the ratio in which Q divides PR.

The sum of first 9 terms of an arithmetic sequence is 45 and the sum of first 18 terms is 171 a) What is the sum of its 10^(th) to 18^(th) terms? b) What is its 5^(th) term? c) Find its 14^(th) term. d). Find the sum of 5^(th) to 14^(th) terms.