Question

Find the sum to n terms of the series $\frac{1}{\mathrm{1.2.3.4}}+\frac{1}{\mathrm{2.3.4.5}}+\frac{1}{\mathrm{3.4.5.6}}+.......$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is D

None of these

At n=1,

Option a $=\frac{1}{\mathrm{3.2.3.4}}....$This can never be the answer

Option b $=\frac{1}{\mathrm{6.3.4.5}}....$This can also never be the answer

Option C $=\frac{1}{\mathrm{4.1.2.3}}....$ This can be the answer

Since an option "none of these" is there , do another check

At n=2, we should get $\frac{1}{24}+\frac{1}{120}$

Put n=2, in option c$=\frac{1}{\mathrm{4.3.2.4}}=\frac{1}{96}\ne \frac{11}{120}$

Hence answer = option d.

Always be careful when there is an option none of these.