Sequences and Series
A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
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Find the sum of the products of the ten numbers ±1,±2,±3,±4,and±5
taking two at a time.
be in G.P. and a+x,b+x,andc+x
in H.P. then find the value of x(a,bandcaredist∈ctνmbers)
If the sequence a1,a2,a3,an,˙
forms an A.P., then prove that
The digits of a positive integer, having three digits, are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.
Find the sum of the series
Find the sum of the following series: (2+1)+1+(2−1)+∞
Prove that b2c2+c2a2+a2+b2>abc×(a+b+c)(a,b,c>0)
If the A.M. between two numbers exceeds their G.M. by 2 and the GM. Exceeds their H.M. by 8/5, find the numbers.