[" b) Find the sum of senies: "],[qquad 1^(2)-2^(2)+3^(2)-4^(2)+cdots*+99^(2)-100^(2)]

. Find the sum of the series 1.2+2.2^(2)+3.2^(2)+...+100.2^(100)

Find the sum to n terms of the series (1)+(1+a)+(1+a+ a^(2)) cdots .

Find the sum to n terms of the series 1^(2)/(1)+(1^(2)+2^(2))/(1+2)+(1^(2)+2^(2)+3^(2))/(1+2+3)+cdots

Find the sum of the series 1.n + 2 .(n-1) + 3.(n-2) + cdots + ( n-1) .2 + n.1.

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 1^(2)+2.2^(2)+3^(2)+2.4^(2)+5^(2)+2.6^(2)+... If B-2A=100 lambda then lambda is equal to (1)232(2)248 (3) 464 (4) 496

Find the sum 1^(2) + (1^(2)+2^(2))+ (1^(2)+2^(2)+3^(2))+ cdots up to 22 nd term.

Find 100 ^(2) - 99^(2) + 98 ^(2) - 97 ^(2) + ...+ 2 ^(2) - 1 ^(2)

Observe the following pattern 2^(2)-1^(2)=2+13^(2)-2^(2)=3+24^(2)-3^(2)=4+35^(2)-4^(2)=5+4 and find the value of 100^(2)-99^(2) (ii) 111^(2)-109^(2)99^(2)-96^(2)

Find the sum to n terms of the series 3//(1^(2) xx2^(2))+5//(2^(2)xx3^(2))+7//(3^(2)xx4^(2))+ cdots .