The sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132 is
The sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132
Simplify the fraction as follow:
12+16+112+120+130+142+156+172+190+1110+1132=(1−12)+(12−13)+(13−14)+(14−15)+(15−16)+(16−17)+(17−18)+(18−19)+(19−110)+(110−111)+(111−112)⇒12+16+112+120+130+142+156+172+190+1110+1132=(1−112)⇒12+16+112+120+130+142+156+172+190+1110+1132=1110Hence, the sum of the fractions 12+16+112+120+130+142+156+172+190+1110+1132 is 1110.
{1(sec2θ−cos2θ)+1(cosec2θ−sin2θ)}(sin2θcos2θ)=1−sin2θcos2θ2+sin2θcos2θ
Determine whether the following numbers are in proportion or not:
13,14,16,17