`1+3+7+15+31+..........................` to `n` terms:

The n^(th) term of the sequence 1/2, 3/4, 7/8, 15/16 is ...................

Find the sum of the indicated number of terms of each of the following geometric progressions: a. (i) sqrt(7),sqrt(21),3sqrt(7) ,…………..n terms. (ii) 2,-1/2,1/8 , …………….n terms 12 terms (iii) 1,1/3,1/9, ………………..,n terms 5 terms b. (i) x^(3),x^(5),x^(7) .......,n terms (x!= +-1) (ii) 1,-a,a^(2),-a^(3) ........, n terms (a!= -1) (iii) x^(2)-y^(2),x-y,(x-y)/(x+y) ................ , n terms (x+y!=1) .

Check whether a] -1 is a term of 33, 31, 29, …..... b] 54 is a term of 3, 9, 15, ........... c] -10 is a term of -3, -5, -7, ......

Sum of the series 1+3+7+15+....... upto n terms.

Find the sums of the indicated number of terms of the following geometric progressions : 1,1/3,1/9 .........., n terms, 5 terms.

1/2+3/4+7/8+15/16+..... t o n terms =

1+ 3+ 7 + 15… n terms =

63, 31, 15, 7, 3, ?

Find the sum of the following series : 3.1^2+5.2^2+7.3^2 + .... to n terms .