Let = 1 60^ 61^ + 1 62^ 63^ + + 1 118^ 119^ Then the value of ( cosec 1^ )^2 is __________

Step-by-step solution

aligned & = _ r -30 ⁵⁹ 1 (2 r )^ (2 r +1)^ & cosec 1^ = _ r -30 ⁵⁹ 1^ (2 r )^ (2 r +1)^ & = _ r -30 ⁵⁹ ( (2 r )^ - (2 r +1)^ ) & = 60^ - 61^ & + 62^ - 63^ & & + (118^ )- (119^ ) & cosec 1^ = 60^ = 1 3 & ( cosec 1^ )^2=3 aligned