If in an A.P. `S_1=6` and `S_7=105`, prove that :
`S_(n),S_(n-3)::(n+3),(n-3)` .

In an A.P., S_(3)=6 and S_(6)=3 prove that: 2(2n+1)S_(n+4)=(n+4)S_(2n+1) .

Let the sum of n, 2n, 3n terms of an A.P. be S_1 , S_2 and S_3 , respectively, show that S_3 = 3(S_2 - S_1)

If in Delta ABC, (a -b) (s-c) = (b -c) (s-a) , prove that r_(1), r_(2), r_(3) are in A.P.

Prove that "^(n-1)C_3+ ^(n-1)C_4 > ^nC_3 if n >7.

If a_1, a_2,a_3,..........., a_n be an A.P. of non-zero terms, prove that : 1/(a_1 a_2)+1/(a_2 a_3)+ ............. + 1/(a_(n-1) a_n)= (n-1)/(a_1 a_n) .

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

Let S_n denote the sum of first n terms of an AP and 3S_n=S_(2n) What is S_(3n):S_n equal to? What is S_(3n):S_(2n) equal to?