Sequences and Series
If a,b and c are positive real numbers then ba+cb+ac is greater than or equal to.
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are in A.P., then prove that the following are also in A.P.
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 to infinity of the series 12+22x+32x2+∞˙
The harmonic mean between two numbers is 21/5, their A.M. ′A′
and G.M. ′G′
satisfy the relation 3A+G2=36.
Then find the sum of square of numbers.
If a>1,b>1 and c>1 are in G.P. then show that 1+(log)ea1,1+(log)eb1,and1+(log)ec1 are in H.P.
How many terms are there in the A.P. 3, 7, 11, ... 407?
If the A.M. of two positive numbers aandb(a>b)
is twice their geometric mean. Prove that : a:b=(2+3):(2−3)˙
then find r=2∑∞T1˙