limn→∞ 1n+1+1n+2+…+16n is equal to

limn→∞ 1n+1+1n+2+…+16n=limn→∞ 1n+1+1n+2+…+1n+5n=limn→∞ ∑r=15n 1n+r=limn→∞ 1n∑r=15n 11+rn∵  Lower limit of r=1∴ Lower limit of integration =limn→∞ 1n=0 ∵ Upper limit of r=5n ∴ Upper limit of integration =limn→∞ 5nn=5 from eq(i) ∫05 11+xdx=[log⁡(1+x)]05=log⁡6−log⁡1=log⁡6