$\left( {M_i^n,{q_i}} \right) \to \left( {{R^k},{q_\infty }} \right)$,but the scaling not?

Suppose $\left( {M_i^n,{q_i}} \right) \to \left( {{R^k},{q_\infty }} \right)$,where $Ri{c_{{M_i}}} \ge - 1/i$.Then $\left( {{\lambda _i}{M_i},{q_i}} \right) \to \left( {{R^k},0} \right)$ for any sequence ${\lambda _i} \to \infty$?I think it's wrong,please give counter examples.And $\left( {{\lambda _i}{M_i},{q_i}} \right) \to \left( {{R^k},0} \right)$ for some sequence ${\lambda _i} \to \infty$? The arrow means Gromov-Hausdorff convergence.

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Without definitions (most notably on the notion of convergence you are using, and what $\lambda_i M_i$ means) your question is not understandable. – Benoît Kloeckner Jun 26 '13 at 18:55
$M_i=\tfrac1i\cdot (\mathbb S^1\times \mathbb R^k)$ and $\lambda_i=i$. – Anton Petrunin Jun 26 '13 at 21:10
You might ask the wrong question, I think you might need an example where the limit space has non-unique tangent cone. But if you insist asking this way, Anton provided an example above. – J. GE Jun 27 '13 at 18:58